Despite playing for most of the second half with a man advantage after Joel Veltman’s sending off, Barca was unable to recover after going in two goals down at the break, though Xavi did score from the penalty spot.
Puyol, who started at right back with Gerard Pique and Javier Mascherano named in the center of defense, says there has to be an improvement.
“If we want to win in Europe, we cannot start games like that,” the defender told reporters. “The idea is to have the ball, but when you have a team up against you which is snapping at your heels and also know how to play the ball around, this is what happens. They came out more intense from the start and were up for it more.
“If you are not up for it enough against teams like that, they will walk all over you.”
Puyol admits his own display was no better than that of his teammates but did feel that his team improved in the second half.
“We had to change and we had 45 minutes to turn the result around," the 35-year-old added. "With the red card and the penalty, Ajax just went into their shells and we couldn't get the equalizer.
“You have to learn from every game and if we want to win things, we know we have to get better. This defeat should make all of us think, including me because I played badly. The first 25 minutes were difficult for everyone and I didn’t feel completely comfortable. The motivation from this loss has to help us to improve."