The North London club had started the game as favourites in front of more than 85,000 supporters at Wembley Stadium, but never managed to recover after conceding two goals in the opening 31 minutes.
Spurs will now travel to CSKA Moscow for their next Champions League fixture and Alli is hoping there is a positive reaction following their toothless showing
"Monaco are a good team but we weren't ruthless enough," Alli told BT Sport.
"The fans came out in numbers and never stopped singing. We need to pick ourselves up and win the next game."