Spurs' 2-0 win over Fulham secured fourth, which would normally guarantee Champions League football.
But Chelsea will snatch that spot away from Spurs if they can beat Bayern Munich in the final of this year's competition.
Although he faces an anxious wait over the club's European place, Redknapp hailed the campaign as a success.
"All you can do is do your job," he said.
"At the start of the year Champions League football, fourth position, I couldn't have asked for more than that.
"I look at the league and I'm not silly - you think Manchester United, Manchester City, Arsenal, Chelsea, Liverpool, who have spent a fortune.
"If we could have got in there we would have been delighted and that is how I am about it all, we have finished fourth and I couldn't be more pleased."
Although results elsewhere ultimately dictated the outcome of Spurs' season - Arsenal's win against West Brom ensured they would finish third - Redknapp claimed he was only interested on his own team's result.
An early goal from Emmanuel Adebayor and a second-half strike from substitute Jermain Defoe earned the hosts a comfortable victory over Fulham and that was enough for the 65-year-old.
He said: "I could hear the crowd cheer (when West Brom took the lead against Arsenal) but I was only concerned with us winning today [Sunday].
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"All that mattered was that we won the game because if we didn't win today, Newcastle could have won at Everton and we'd have been fifth. It was just important we won the game and that was the only concern I had."
Redknapp may have led Spurs back into the league's top four but he reckons the feat will only become more and more difficult in the coming years.
"When we finished fourth (in 2010) Man City were just arriving. It is going to be even more difficult next year," he said.
"Man United and Man City are not going to be out of the top four: that's impossible. So you are looking for two places. Chelsea, I don't think Mr Abramovich will stand for them finishing outside the top four again.
"So suddenly there is Arsenal, us, Liverpool, Newcastle all scrapping and who knows a Russian could come along and buy someone like Wigan and then they will be pushing for the league - that's how it works isn't it?"
England midfielder Scott Parker missed the match as he continues to fight an Achilles injury and it is still unsure whether he will be fit for selection ahead of this summer's European Championships.
"He has got an Achilles injury and is going to have an injection on it tomorrow and they are hoping that with six or seven days rest it will be okay," Redknapp said.
"If it doesn't clear up he wouldn't be fit. If he had to have an operation it would be long term, so we will have to wait and see how he is."
Fulham boss Martin Jol felt his side could have done better against his former club in a fixture that was relatively meaningless to the Cottagers.
"If you concede a goal after 90 seconds it is always difficult, you make it difficult for yourselves," he said.
"We know that if you come to a place like White Hart Lane you have to play with flair and not be intimidated.
"In the first half an hour they were better, stronger and sharper and had everything to play for.
"We created a few chances and then they scored again after a bad clearance and that is exactly what you shouldn't do."
Jol, who took over as Fulham boss last June was happy with a ninth-placed finish in the final standings.
"I think in hindsight if you see the gap with the other teams - equal on points with Liverpool and five points clear of the others you could say we were the best of the rest. It is not fantastic but it is good," he said.
"I would like to have had a draw here and maybe be eighth but ninth is fantastic."