Manuel Pellegrini's West Ham United side have now lost their last three matches on the bounce.
West Ham felt hard done by after they went away with a 2-1 defeat from Old Trafford at the weekend.
West Ham were arguably the better team against Manchester United, but they were undone by two penalties.
While Ryan Fredericks could have few complaints about giving away a spot kick, Snodgrass felt that the decision against him was incorrect.
The Scottish international went into a challenge on Juan Mata and felt that he had been harshly treated.
However, Carragher believes that Snodgrass did commit a foul and that United deserved the penalty that was awarded.
He said: “Everyone else has said no, but I think it is. Snodgrass has come in from behind and not got the ball. Mata is ready to strike the ball, doesn’t know that the challenge is coming and gets knocked over. I think it was a penalty.”
West Ham’s defeat to United means that they have now lost their last three matches on the bounce.
Manuel Pellegrini’s side are currently in 11th place in the Premier League table, with their next match coming against Leicester City at the weekend.