Spurs' first shot at a trophy ended at the semi-final stage as they were beaten on penalties by Chelsea after the Blues overturned a 1-0 first-leg deficit at Stamford Bridge.
The tie ended 2-2 on aggregate before Eric Dier and Lucas Moura both failed with their spot-kicks, handing Chelsea a place in the final against holders Manchester City.
"The season is long and we need to move on," he told the club's website.
"It's another game in three days [in the FA Cup fourth round against Crystal Palace] and the season isn't finished.
"We're out of this competition, that's hard for us but we need to keep going forward, always."
Fellow teammate Jan Vertonghen is confident Spurs will bounce back from the disappointment and end their 11-year wait for silverware.
"I think it was a brilliant performance from us, obviously Chelsea played well, so it's a shame," he told Spurs TV.
"We probably both think that we deserved to win. I think that Tottenham definitely deserved to go to the final but this is life.
"We have a lot of chances to come back and we will, this is what we do. We've had it in the past but we're so strong mentally and physically in every single way, that is what makes us good."
Next up for Mauricio Pochettino's men is a trip to Crystal Palace in the FA Cup fourth round on Sunday, before a return to Premier League duties against Watford three days later.