Spurs were beaten 1-0 by Manchester City at Eastlands on Tuesday night as Roberto Mancini's side secured a top four finish after missing out to Spurs last season.
Tottenham will also miss out on sixth if they lose to Liverpool on Saturday and they go to Anfield in dreadful form having won just once in their last 13 games in all competitions while picking up just nine points from their last 10 league outings.
“I'm going to go and commit suicide, it's so sad,” Redknapp quipped after the game.
“We've played well but have just not been able to finish teams off and have drawn a lot. It's been a great season and people shouldn't just look at the last few games.
“We've been in good form, much better than the results have shown.
Tottenham enjoyed a successful season in the Champions League this season but their league form suffered following their eventual exit at the hand of Real Madrid at the quarter-final stage.
Redknapp admits his side have not scored as many goals as he would have liked this season but insists it has just been a freak season in front of goals for strikers Peter Crouch, Roman Pavlyuchenko and Jermain Defoe.
He added: “It's not a lack of killer instinct. We've got strikers who normally score lots of goals and unfortunately this year we haven't scored as many as usual.
“Sometimes it goes your way as goalscorers and unfortunately we haven't scored enough goals.
“Over the whole season it's been a great season. Probably the best Tottenham have had in God knows how long.”
Redknapp feels he needs “one or two” signings in the summer to boost Spurs' chances of the club finishing in the top four next year – but he knows he faces a tough task against the spending might of City and a resurgent Liverpool team.
“I don't know if we've got any money to spend,” Redknapp admitted. “I've not asked the chairman yet. We will have to wait and see – if not we will get on with it and go again. We will be strong again next year.
“We need to shift a few in the summer and bring one or two in. Eight of that team were bottom of the league [when Redknapp was appointed in October 2008]. We had two point from eight games, so we've improved the players here rather than gone out and spent money.
“It's difficult to get in the top four. Man United, Chelsea and Arsenal are never going to drop out so there is one place. Man City have billions to spend and Liverpool are getting better. That top four is difficult to make.
“We hadn't made it before and this was our first year in it.”