Spurs sit bottom of Group E after slipping to a 2-1 opening defeat against Monaco in front of 85,011 fans at Wembley.
The crowd set a new English club record for a home attendance and Mauricio Pochettino's men dominated much of the contest, only to pay the price for sloppiness at both ends.
Harry Kane and Son Heung-min both missed chances, while Erik Lamela gave away possession in the lead-up to Monaco's first goal before Jan Vertonghen and Ben Davies failed to clear the cross for the second.
The French side, in contrast, were clinical as Bernardo Silva and Thomas Lemar put the visitors two up, with Toby Alderweireld's header proving nothing more than a consolation.
"We didn't help ourselves in the first half," Alli said
"In the second half we dominated it but we weren't clinical enough
I think we did do enough to win the game, but unfortunately it wasn't our night
"We need to make sure we learn from our mistakes and start games quicker and brighter
We need to finish strongly as well and be a lot more clinical."
Alli started the game in a deeper central midfield spot next to Eric Dier but was far more influential when pushed further forward in the second half, after Son had been replaced by Mousa Dembele.
Pochettino has deployed Alli both centrally and left of the attacking three, as well as in a deeper role, but the 20-year-old insists he is comfortable in any position.
"When I was at MK Dons I played all the games in centre midfield so it's not like it's new to me," Alli said
"I'm happy to play anywhere for the team."
Dembele's return was one positive from an otherwise disappointing night for Tottenham as the Belgian, who has been suspended in the Premier League, made his first competitive appearance of the season.
The midfielder was later seen hobbling as he left the stadium but he indicated it was nothing serious and should be available against Sunderland on Sunday.
"He's a fantastic player
There's no doubt about that," Alli said.
"He's a brilliant player and we're excited to have him back but Victor (Wanyama) has done really well since he's come in and Eric as well in centre midfield.
"With the amount of games we've got coming up it's important to have a lot of depth in the squad and it's good that he can come back and fight for his place in the team."
Alli's partnership with Kane played an integral part in Tottenham's success last season but Kane is yet to hit top form.
The 23-year-old was typically busy against Monaco but he snatched at a chance late on and has now scored just once in six games.
Kane has made a habit of silencing his doubters - he scored one in nine at the start of last season before winning the Premier League Golden Boot - and says he is ready to do so again.
"I sliced it which made it go in the middle of the goal
It's disappointing," Kane said of his late chance at Wembley.
"I back myself in those situations
It's just one of those I didn't connect right with.
"I scored a few days ago, it's no problem
People will talk and say things about my ability but I know what I'm capable of.
"I've just got to keep working hard and I know the goals will come."
Source : PA
Source: PA