A third-placed finish under the Argentinian last season - after a title bid ran out of steam - secured a return to European football's top table for the first time since 2010-11, but Tuesday's 2-1 defeat to Monaco saw Spurs crash out with one group match still remaining.
Goals from Djibril Sidibe and Thomas Lemar either side of Harry Kane's penalty condemned Pochettino's side to a third loss in five Group E matches, with only a place in the Europa League left to play for.
And Pochettino felt his squad has lacked the strength in depth to be able to compete on both European and domestic fronts.
"Maybe after five games we don't show quality enough to be competitive in the Premier League and Champions League," he said in his post-match media conference.
"It was tough and that is good for us to learn and try for the future if next season we're in the Champions League to make some changes.
"It was a good challenge for us to compete in the Champions League and to show our real level, that is always important.
"We reduced the gap at the top of the Premier League and that was our objective but to be competitive in the Premier League and Champions League we need to show more and maybe add more quality to our squad.
"We have quality yes, to compete in the Premier League yes, but to share [compete on multiple fronts]? Maybe I can say we struggle a little bit.
"I am disappointed and upset with that game but in the same way I am quiet and calm because our project is not finished today, it's only just started. It's the first steps, the objective is to be in the Champions League regularly for when we get the new stadium."
Pochettino rejected the notion it may serve the club better to miss out on Europa League qualification and concentrate on their domestic fortunes.
"It's good for the club to be in the Europa League and to go further in the competition," he said.
"Tomorrow is another day and we need to look forward. We're in a good position in the Premier League and we need to compete on Saturday against Chelsea. It's another tough game and we need to lift the players and try to win the game."