Cole, left out of the starting line-up to accommodate new £15million striker Nicolas Anelka, believes the setback can only help them become tougher.
Cole said: "We are disappointed but we have got to pick ourselves up for the next game.
"We will go away and digest this game but it is disappointing for everyone at the club to lose in the final. We've not experienced that before as a group and it can only make us stronger now.
"We will wash ourselves of this game and concentrate on the next one. Tottenham are a very good side and give them credit for winning. But we have to move on."