The Spurs boss also spoke of the importance of Chelsea's upcoming Champions League final as well as Emmanuel Adebayor's future as thoughts turn to summer transfers
The Spurs manager expressed no regret that his side blew a significant lead over rivals Arsenal but pointed to the difficult task he faced at the beginning of the campaign and suggested fans should be happy.
Redknapp told reporters: “We finished fourth – I couldn't be more pleased with what the players have done here this year.
“If people start getting carried away with Tottenham should be doing then they want a reality check.”
With Arsenal facing West Brom at the Hawthorns at the same time, the reaction of the crowd ensured Redknapp and his staff knew the score in the battle for third.
He said: “I could hear the crowd cheer but I was only concerned about us winning today.
“That's all that mattered – that we won the game. I thought if we don't win today, Newcastle could win at Everton and suddenly you'll be fifth. "
Two years ago, Spurs' fourth-place finish meant Champions League qualification but with Chelsea in the final of Europe's premier competition, attention turns to Munich on Saturday.
“This is a bigger achievement than two years ago because Manchester City are so strong,” Redknapp added.
“When we finished fourth they were just getting going. They had Tevez but it was different. It will be more difficult next year. Man Utd and Man City aren't going to be outside the top four – that's impossible.
“I don't think Mr Abramovich is going to stand for them [Chelsea] being out of the top four next year. So there's three teams. Suddenly it's Arsenal, us, Liverpool, Newcastle improving – we're all scrapping.”
Redknapp also revealed he will cast aside family loyalty and support Bayern Munich in a game he is attending.
“Of course it's difficult but it's no more than Frank [Lampard] would if he was involved with Chelsea,” he said.
“We're professional – he knows I want Tottenham to play in the Champions League next year. I want to beat Chelsea whether Frank plays or not.
“When I was manager of West Ham, we played Liverpool when Jamie was playing for them but I still wanted West Ham to win.
“My allegiances are with Tottenham only. I want to see us in the Champions League next year.”
The club's intentions over the summer should become clear after their fate is sealed, but Redknapp spoke about the future of striker Emmanuel Adebayor, who looks to have played his final game for the club.
He said: “It was only a loan, and that's up. It's up to the chairman now, whether we could loan him again. I'd like to keep him, he's done great for us but I don't know if we can afford him. We don't pay those wages.
“The only way would be if the chairman could do another clever deal like we did this year. [Parent club Manchester City] want nothing to do with him, they don't want to see him ever again probably. They want to see him out the way and gone.”
Looking at the overall picture, Redknapp was quick to point out that further investment will be needed if Tottenham are going to remain in the top four.
“If you want to try and get in the Champions League next year you have to improve,” he explained.
“Chelsea didn't get in the Champions League this year but that doesn't mean they're not going to improve in the summer to get in next year.
“If you want Champions League football you've got to try as best you can to hang onto the coat tails of those top clubs.
“In the last ten weeks or so, Ledley's not been fit. William Gallas has carried injuries and played.
“I took Ryan Nelsen on a free from Blackburn. Even today we had Gareth Bale going left-back, Adam Smith comes on at right-back.
“Nelsen, who's a great professional, ends up centre-half when [Younes] Kaboul goes off.”
Redknapp referred to Kaboul's knee problem, saying "it doesn't look great", but took the time to discuss the future of another centre-half, Steven Caulker, currently on loan at Swansea.
Asked whether he would return to the first-team squad next year, Redknapp said: “It's not going to be any good bringing him back and putting him in the squad.
“You either bring him back and play him or leave him on loan. He's learning the game still, done a great job and improved at Swansea but he needs to continue playing.
“It depends what happens here in the summer. If you're not going to start him he's better off playing another year in the Premier League.”