Spurs had been in prime position to claim one of the four spots on offer to Premier League clubs, but following today's 2-2 draw at home with Everton, the likes of Arsenal and Chelsea are now in close contention.
As a result, Villas-Boas believes that his side may have to wait until May to confirm their place in Europe's top competition.
"It looks like it will go down to the wire at the end of the season for these Champions League spots. It's part of the game. Everything shifts very, very quickly in the Premier League but we have been in this position before and you have to deal with the pressure," he told BBC Sport.
Spurs are currently fourth in the Premier League standings, two points better off than rivals Arsenal in fifth.