The Eagles went 2-0 up in the first-half through a John Stones own goal and a Joachim Andersen header, before City fought back in the second-half courtesy of a deflected strike from Bernardo Silva and an Erling Haaland hat-trick.
"I'm disappointed of course," Vieira said of the result.
"Because in a game of football when you lead 2-0 at half-time, you expect to get something from the game.
"But today was a special team we were facing, so much quality collectively and individually.
"And in the second-half when they raised their game it was really difficult for us to cope with it.
"But today I think we showed character and discipline.
"And we can be unlucky to go back home with nothing.
"The first-half was the perfect performance away from home.
"I think we were well-disciplined. Jordan [Ayew], Ebs [Ebere Eze] and [Odsonne] Edouard worked really well and we closed down all the spaces to not allow them to create those chances.
"And in the second-half I think physically we dropped a little bit. I think we didn't put enough pressure on the ball, and that allowed them to move the ball quicker from one side to the other and create the situation where they felt comfortable, create those chances and score goals.
"It was difficult [in the second-half], the momentum was on their side and it was really difficult for the [Palace] players who came on.
"But overall we showed character and the quality of the opposition made the difference in the end.
"When you are disappointed what you want is to bounce back straightaway and the game on Tuesday [against Brentford in the Premier League] will be important for us to bounce back and try to win it.
"We can be really proud of the fans making their way to the stadium to support the team in a really difficult [travel] period.
"From the players and myself we really want to thank them for making that effort and to be behind us."