Watford opened the scoring when Etienne Capoue slotted home from Daryl Janmaat's cut-back but Marcus Rashford drew United level.
However in the second-half substitute Juan Zuniga scored with his first touch and in the final seconds of the game captain Troy Deeney converted a penalty to secure the win.
Speaking after the game, Mourinho said the team have to stop making individual errors and called on his players to raise their game. The United boss also blamed the referee and a lack of luck for his team.
“I reflect on three factors from the match, but only one of them I can improve.
Manchester United manager Jose Mourinho and assistant manager Rui Faria
Image credit: Reuters
"The first factor depends on ourselves, it relates to our individual mistakes and collective mistakes as individual players and as a team. We have to improve something, it is in our hands.
"The second factor is the referee and I can’t control their mistakes, The story of the game is the result and not the ridiculous situation of the first goal.
"The third factor is luck, we didn’t have it. We were the best team when we lost. Heurelho Gomes made a phenomenal save from a Zlatan Ibrahimovic header."
Mourinho didn't specifically name any players but captain Wayne Rooney and midfielder Marouane Fellaini, who gave away the late penalty, both came in for plenty of criticism from the club's fans.
Mourinho has never been afraid to criticise referees during his career and he felt that there was a foul by Watford defender Miguel Britos in the build-up to the game's opening goal which Michael Oliver failed to give a free-kick for.
"That’s an obvious situation. I think there is no debate, no controversy. I think that is an obvious situation, like it was obvious last week against Man City but it’s something I don’t control and I cannot even be critical of.
"In the eyes of everyone, it doesn't matter whether you're a Manchester United fan or a Watford fan or whatever, it was obvious."