Spurs never got close to what would have been a miraculous comeback against Real Madrid at White Hart Lane on Wednesday by overturning the 4-0 first leg defeat they suffered at the Santiago Bernabeu last week.
Instead, a mistake from goalkeeper Heurelho Gomes gifted Cristiano Ronaldo one of the softest goals he will ever score and Real won 1-0 to complete a 5-0 aggregate rout and set up an all-Spanish semi-final against arch-rivals Barcelona.
Redknapp echoed the mood of his upbeat players and Spurs fans afterwards, however, when he said their first taste of the Champions League left them hungry for more.
After a dramatic 6-3 aggregate victory over Young Boys of Berne in the qualifier, Spurs beat champions Inter Milan and topped their group, then beat seven-time champions AC Milan in the round of 16 before finally bowing out to the nine-times European champions.
"We've seen some great football in the Champions League this year, home and away," Redknapp said. "First season in the Champions League, to come as far as we have and to play the way we have played throughout the run has been great for everybody.
"It's been a great experience for the players and myself. We've all enjoyed it very much - even tonight's game which was very evenly balanced.
"It's very difficult to retain that top-four spot but that's something we've got to aim to do at Tottenham. If we can make the top four again, it would be a great achievement."
KEEP IMPROVING
Tottenham are just outside the Premier League's top at the moment, three points behind fourth-placed Manchester City, who they pipped to the Champions League last season, with a game in hand, and five points behind third-placed Chelsea.
They still have to play away at City and Chelsea.
"It will be even harder this year than it was last year," Redknapp said. "Manchester City finished two points behind us last year, then went out and spent about 150 million pounds to try and finish above us this year.
"But this is something we must aim to do every year at Tottenham, and we have to keep improving now if we want that.
"I still think we've got a big chance. We've got tough games. "We've got Arsenal here next week, then we've got Chelsea, we've got to go to Man City."
Spurs have won plaudits across Europe for the attacking football they have played which saw them finish as joint top scorers with 18 goals in the group stage.
However, the goals did dry up in the knockout rounds, scoring just once at Milan, and clearly they will have to strengthen in the summer to keep pace.
Their targets will be some added firepower in attack, after generally misfiring campaigns from Jermain Defoe, Roman Pavlyuchenko and Peter Crouch, whose dismissal early in the first leg helped give Real the control they never relinquished.
Hanging on to the likes of Luka Modric and Gareth Bale will also be priorities but for now Redknapp is just concerned with the final eight games of the season.
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