The Eagles were 3-0 down at half time after Wandsworth-born Michail Antonio opened the scoring and Manuel Lanzini scored a double.
Michael Olise sparked a second-half fightback – setting up Odsonne Edouard in the 83rd minute before scoring a free-kick in the 90th minute.
It was the second time that Vieira’s side had fallen to defeat at Selhurst Park this season.
When asked by Sky Sports if the scoreline reflected the story of the match, Vieira said: “It’s really difficult because tonight we played some good football and created a number of chances to win the game.
“I’m really disappointed because we were the better team. The difference between the two sides is that they’ve been building the team for a couple of years – it is a mature team.
“The experience of this team allowed them to win. At times we were naive. We created chances, and we were unlucky. We had the best first chance of the game and hit the post. We have to learn from those games and improve. Playing well is not good enough to win.”
Luka Milivojevic was adjudged to have deliberately handled the ball in added time of the first half after referee Darren England consulted VAR. Lanzini tucked away the penalty to give the Hammers their third goal of the first half.
Vieira was given a yellow card at full time for his protests.
Speaking on the penalty, the Frenchman added: “It was the referee’s decision. From where I was, it was difficult to say if it was a penalty at first, but I saw it after and thought it was a penalty.”
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