Knocking both Manchester clubs out of cup competitions more than made up for the woeful defeat at Bolton which had manager Kenny Dalglish publicly criticising his players.
However, Skrtel believes the performances put in against City and United have to become the norm rather than the exception if the Reds are to re-ignite their bid for a top-four finish.
Having already lost to the likes of Wanderers, Fulham and Stoke - and drawn against Wigan, Norwich, Swansea and Blackburn - the Slovakia international knows what pitfalls await displays which are not up to standard.
"The performance against Bolton wasn't the best but the key before the games against City and United was to forget about the Bolton game," he said.
"I think those two results (against City and United) were the perfect response to that criticism.
"They were two difficult games but now it is a league game and we need to repeat the performance from those two games.
"We have to be focused on the game against Wolves because it will be a similar game to that against Bolton.
"They will be physical and we need to deal with this and get a result there."
Dirk Kuyt, scorer of the winning goal against Manchester United in their FA Cup fourth-round tie on Saturday, agreed with Skrtel.
"I think we set the standard this week," said the Holland international. "Everyone was really disappointed with the Bolton game and how we didn't put the effort into the game and it was not at the level we want - or used - to play.
"I think we have proved many times we can compete with the best teams and, with respect, we also need to play well against the other teams so the next game is very important against Wolves."
Dalglish did not think his players needed to be reminded of their obligations but he pointed out the minimum expectations.
"You may not always play to the best of your ability but you should always compete to the best of your ability, that is all you can ask," said the Scot.
"The bar has always been set high here and most of the time they have got up to the bar.
"There have been a couple of times when we have not done it but I suppose that is natural.
"If we are going to get anything out of the game we have to put in the same level of performance.
"I don't think people are showing signs of fatigue because we have changed and moved people around.
"Some people have greater demands on them than others - everyone has different levels of fitness - but I don't think there is any problem with fitness."
