Spurs lost 4-1 in a penalty shootout, after the game finished 2-2 following extra time, 4-4 on aggregate.
Adebayor missed the final penalty, which saw Basel go through to the semi-final of the competition, where they will face Chelsea.
"It's tough. You run around for 120 minutes, you give everything you have in your stomach, you are tired, you play with 10 men for 30 minutes and at the end of the day you have to take a penalty," said Adebayor.
"The pressure is there when you take the ball. It's not the reason why we missed. We had to score, but it's not easy for us.
"I am very disappointed, but that's football. You just have to keep focused and keep going."
Adebayor has scored six goals in 28 appearances for Tottenham this season.