After spending all week in Southwark Crown Court this week, Redknapp returned to the dugout to find his Tottenham team in disarray.
The Premier League title chasers put on a woeful display in the first half and only went through thanks to Rafael van der Vaart's fortuitous 30-yard drive just before half-time.
Watford, who sit 35 places below Spurs in the league ladder, looked much the sharper side and rattled the woodwork twice in the second half.
Lively striker Marvin Sordell was unlucky not to impress his suitors after being foiled on a number of occasions by Carlo Cudicini and Redknapp conceded it was a minor miracle that his team progressed.
"I thought we were fantastic," Redknapp joked. "The football was mind-blowing. I have never been so excited watching us play. It was unbelievable."
He added: "How we won that game I will never know. It's better to be lucky than good sometimes and we were lucky, that's for sure.
"We never played - we didn't pass the ball - and they played really well. They pressed us and passed it so how they lost I don't know.
"It is difficult to put your finger on it. We always move the ball well but we were giving it away. We just never got going.
"We were hanging on in the end, just hanging on. That game was as tough as any we have had away from home. We have a great away record normally but we just rode our luck."
Redknapp has been almost entirely cut off from his role as Spurs boss for the last five days and will be so again for the next week as his trial is expected to continue until Friday at the earliest.
The 64-year-old Redknapp, who denies two charges of tax evasion, named a strong starting XI that included the likes of Van der Vaart, Luka Modric, Jermain Defoe and Emmanuel Adebayor but they put on a completely different display to the one which saw Spurs run Manchester City close last weekend.
Despite this performance, Redknapp still thinks his men can go on to win the FA Cup this year - a feat the club have not managed in 21 years.
"It's a big opportunity for us this year, Redknapp said.
"We can beat anybody in the country and I didn't want to throw that away by making wholesale changes. We didn't play well but that certainly wasn't through messing around with the team."
Watford will rightly earn many plaudits for a display that defied their position of 18th in the npower Championship.
Hornets boss Sean Dyche, who is in his first year in management, was proud of his team's efforts.
"I felt we were good value," he said. "We worked hard to get reward from our performance and we so nearly did. But credit to them, they found a way to win and sometimes that's what you need to do.
"We are disappointed not to get anything from the game. The minimum we deserved was a replay and we could have won it but there were a lot of positives. Six who started were Academy products and that's important to our club."
Dyche's team would have earned a replay had Sean Murray and captain John Eustace scored instead of hitting the woodwork and sought-after duo Sordell and Adrian Mariappa also played well.
Newcastle are interested in signing Mariappa, but Dyche is not resigned to losing the centre-back just yet ahead of Tuesday's transfer deadline.
"We like what he does at this club and there is no decision to make at the moment," Dyche said.
"There is talk of loads of clubs being interested which in a way is a positive for us because we like to think we are a club that develops and improves players."
