"I thought maybe the goal wasn't going to come and we'd go to Burnley with the extra point in the bag, which would have been a good situation, but this is perfect to finish it here," he added.
Even third place, and therefore finishing above north London rivals Arsenal for the first time since the 1994-95 season, is achievable for Spurs, although they need to make up a two-point deficit on the Gunners.
Reaching at least the qualifying stages of the Champions League marks a remarkable turnaround in Spurs' fortunes since Redknapp took the helm. Tottenham were bottom of the Premier League with two points from eight games when Redknapp left Portsmouth to replace Juande Ramos as manager in October 2008.
"I think to finish third would be asking a lot but fourth is a great position for us," said Redknapp.
"We'll have to have a look in the summer and see where we can improve if we have to, but we've got good players here. I think there might be eight boys in the preliminary squad for England."
Redknapp said his positive approach at Eastlands - starting with two strikers and the likes of Aaron Lennon in the starting line-up - had paid rich dividends, with Peter Crouch grabbing a deserved winner on 82 minutes.
"Most people probably thought we'll come here and take a point but I picked the most attacking team you could ever wish to see," he told BBC Sport.
"We came here to a hot atmosphere and got at them and we deserved the win.
"Crouchy was top class and led the line and he deserved the goal. I also think Jermain Defoe had his best performance away from home for some time.
Asked about centre-back Ledley King, Redknapp said: "What a player, he's got to go to the World Cup, but Michael Dawson as well - the two of them tonight were just fantastic. You've got to put them in your squad."
Spurs chairman Daniel Levy hailed the turnaround that has led to the club securing a top-four place as "an amazing achievement".
Redknapp drenched by Spurs squad
"Harry's done a great job and we're very proud of him and the whole team," he said.
Asked what Champions League qualification meant for the club, Levy said: "Only time will tell but in the process of considering a new stadium it's come at the right time.
"This is such an achievement for us to be there is really quite something."
Crouch, who was part of the Liverpool side that lost the 2007 Champions League final to AC Milan, stated: "The dressing room was buzzing afterwards but, when things settle down, I think we will realise the magnitude of our achievement.
"The job is not done yet because we still have to qualify but just to be in fourth place considering the teams we were up against is a great achievement, and probably one of the best of my career."
Defoe added: "It's fantastic. The lads have put in so much hard work over the course of the season and we've got our reward. It is a fantastic feeling to have made it."
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