The loss at Old Trafford confirmed Manchester City as Premier League champions, with Jay Rodriguez scoring the only goal of the match as the league's bottom club picked up a surprise three points.
Vidic, who won five Premier League titles during his time at United, has said that he would like to see his former club "playing faster", particularly against the lesser teams.
"It was too slow, which was disappointing. That is my worry, I'd like to see United playing faster, quicker with the ball. It's too many touches, that's the problem, especially against smaller teams," Vidic told Sky Sports News.
"They have a good team, good players, but sometimes I think the players have to show desire, show energy, run more than other teams.
"They didn't move well without the ball, they didn't move fast. The players didn't perform the way they wanted. It's sad to see Man United lose at home to West Brom, a team who have won just three games all season."
United will take on Tottenham Hotspur at Wembley in the semi-finals of the FA Cup this weekend.