Atletico Madrid striker Morata, who was on-loan with Juventus last season, missed a big chance in the first half and was on the receiving end of yet more whistles and boos from his own supporters, and not for the first time this summer.
"Being whistled is nothing new," Laporte said after the match. "There can be no doubting a striker like Alvaro, who has shown so much.
"It's true that he hasn't had a successful night but in the next few games he'll shut people's mouths.
"We were missing a goal today but one day we'll score five and on another we won't score any. We're not worried abut having top forward, it was just today that it didn't go our way but it will in another game.
"People can be nervous, but we've proven ourselves to be a strong team with the ball and nobody wants to win more than we do."
The result, though, was disappointing and the Manchester City defender couldn't dispute that.
"There are bad feelings," Laporte admitted. "We played well, dominated for a lot of it and we had chances.
"But we have to think about the next two games and try to do better. If we play 10 games like this, then we'll win nine of them. This time we drew."