Alli was booked for simulation in the second half of the Europa League second leg and will be unavailable for the first leg of the next round, which will take place on March 10.
Pochettino said: "I think like you, like all the people in the stadium, it was not a yellow card.
"I think it was a foul for us, but sometimes the referee gets it wrong. We will miss him for the first leg but we are a strong team
"We have a lot of games ahead and we will start to compete in the Europa League again - and we will try and play as well in the next round."
Spurs went out of the FA Cup at the weekend after losing 1-0 to Crystal Palace and Pochettino was pleased with how his side bounced back from the defeat to keep their trophy dreams alive.
He said: "I think that the performance was fantastic, the job is done and now we are in the next round, as was our objective before the game.
"The competition is done for now and we need to be ready for Sunday (their Premier League match against Swansea)."
Tottenham were missing star striker Harry Kane on Thursday due to a broken nose he picked up in the defeat to Palace but Pochettino believes it is vital his side show they are good enough without him.
He said: "Harry Kane is very important for us but today it was impossible for him to be available.
"We have played enough and we were competitive in every way and after what I have seen today, I am very proud of the players."
Source: PA