Adkins remains behind Rodriguez
Saint-Etienne coach Christophe Galtier labelled his players "a team of men" after they reached the final of the Coupe de la Ligue on penalties.
ASSE controlled their semi-final against Lille throughout but a determined performance from goalkeeper Steeve Elana ensured the match went to a shoot-out.
Idrissa Gueye missed the crucial penalty to send St Etienne through 7-6 and book the club's first ever Stade de France final against the winner of Wednesday's match between Rennes and Montpellier.
"We have a team of men," Galtier told reporters. "We came across a good goalkeeper but overall we played good football, we were very dynamic and we pushed forward.
"The players prepared for the match in the best possible way, but then they showed they were men on the pitch.
"The goal was at least to get to the Stade de France and now we will see what happens there."
Saint-Etienne had to sweat for their progress as Elana made excellent first-half saves from Yohan Mollo and Fabien Lemoine, while Brandao missed the first of many good chances on a dismal night for him personally.
Early in the second half, Pierre-Emerick Aubameyang was denied at point-blank range by Elana and then by the Lille defence, while Marko Basa blocked Mollo's shot.
Brandao let another clear chance slip away when he failed to convert after good work by Lemoine. Shortly afterwards, the Brazilian was substituted and stormed straight down the tunnel.
His replacement Renaud Cohade was denied by Elana but Lille could have snatched victory late on when former ASSE midfielder Dimitri Payet fired against the outside of the post.
"I am really proud of my players. I have a lot of emotions," Galtier said.
"Everyone has a smile. If we can give happiness and pride to be supporters of AS Saint-Etienne it is a good thing."
Lille boss Rudi Garcia felt the penalty defeat was rough justice on his side, although admitted they failed to test ASSE's defence often enough.
"It's cruel but that's the Cup," he said.
"We had our finger on qualification, but we did not have enough punch in attack throughout even though we were very good defensively."
The Black Cats marked the 40th anniversary of their last FA Cup triumph with a tame defeat to Bolton on Tuesday night.
Two second-half goals from Marvin Sordell sent the Championship side through to an FA Cup fourth-round clash at home to Everton and left O'Neill to look ahead to a gruelling battle to secure his side's top-flight future.
O'Neill said: "The fact it is 40 years since we've won a trophy is far too long. We enjoyed a really good run last season and put some big results together in January and February, then we played Everton and were disappointing - but that was a quarter-final.
"Here we had the opportunity to play Everton again and we didn't take it and it is really disappointing.
"We're going to have to get it (consistency). This is a big club and we shouldn't be spending 40 years without winning something, we really shouldn't."
Laudrup arrived at the Liberty Stadium in the summer with a reputation for producing sides who played attractive, attacking football and scored plenty of goals, but were also liable to concede at the other end.
The Swans are unquestionably a greater attacking threat this term, mainly thanks to the goalscoring heroics of Michu, but their excellent run of just two defeats in 17 games has been based upon a solid defensive foundation.
Ashley Williams, Chico Flores and young Ben Davies have excelled as part of the back four, with Angel Rangel, Garry Monk and Dwight Tiendalli also making notable contributions.
Such has been the level of performance, Swansea have conceded just 11 goals in nine games away from home in the league this season, which along with Arsenal is the joint-lowest total in the top flight.
Having triumphed 2-0 at the Emirates Stadium earlier this season, Laudrup knows more of the defending seen on that occasion, and in keeping clean sheets at Chelsea and Everton, will be required on Wednesday night to secure safe passage through to an FA Cup fourth-round meeting at Brighton.
He said: "We have shown throughout the season, but particularly in the last two games, how solid we are. I have even been a bit surprised by how solid we have looked defending deep.
"I always try to say not to defend so deep. Against Chelsea, it is one thing as they don't play many balls into the box, but Everton do with a lot of big guys up there and we did great and and that is really good to see.
"In 11 away games we have only conceded nine goals which is quite good for a manager who always played up front.
"But the players know if they are a little relaxed against the big teams you can get hurt really bad."
Wednesday night's third-round replay has added to an already hectic month for the Swans, with the Capital One Cup semi-final with Chelsea also increasing their workload.
But Laudrup is adamant the congestion does not put the FA Cup at the bottom of his list of priorities.
He said: "The 11 or 14 who play will do everything to win and Arsenal are the same.
"I cannot tell the players who go out 'just play at 50 per cent because we don't really care about winning this game', you cannot do that.
"In the first game in this tie, we were up and then we were down.
"We could have won the game and lost the game but we fought and got a draw in the end and it shows that the 11 who go on the pitch will give their all."
Rodriguez won the decisive penalty in Saturday's 1-0 Premier League win over Aston Villa at Villa Park.
When asked if he felt the former Burnley forward had dived, Adkins had a bullish response: "He's not a diver. We don't advocate diving here whatsoever.
"We could have had seven or eight penalties this season, we don't surround the referee, we allow the referees to make the decisions.
"When you look at the one at the weekend there was intent there, it was a poor challenge from the defender (Enda Stevens), correct there is no contact made but it's still a poor challenge from the defender - Jay is a young lad who is so enthusiastic."
Adkins, speaking ahead of Saints' clash at Chelsea on Wednesday night, also said that his team must continue to create situations where the officials are forced into making big decisions.
He said: "All we need to do is keep getting the ball in the penalty area in a way we give defenders decisions to make whether to challenge or not and give refs decisions whether to give penalties or not.
"Seven or eight times clearly we should have had penalties. That's the reality of football."