Anthony Martial added to Ashley Young's double as the Red Devils took a three-goal lead at Vicarage Road on Tuesday, but Romelu Lukaku and Paul Pogba were among those who failed to add to their tally.
Troy Deeney rolled home a penalty with 13 minutes remaining after Marcos Rojo's foul on Roberto Pereyra, before Abdoulaye Doucoure set up a tense finale.
Jesse Lingard ended Watford's hopes of salvaging a result from the match with a tremendous solo effort in the 86th minute, but Mourinho was frustrated his players had not put the game to bed beforehand.
"The second half should be five or six nil and it was even easier to score goals in the second half than in the first, but we missed these chances and this is football," the United boss told BT Sport.
"Out of nothing, penalty, and 3-1 and then the game is a different one. It is a match to win comfortably and in the end with the 3-2 the game is in a grey zone and Jesse had that fantastic initiative and won the game.
"We missed the 4-0 also in a great action in the end of the first half and in the second half we had a great high press to recover the ball high and Lukaku also had that one, and Paul's header is a free header – we had lots of chances.
"But then out of nothing 3-1 and the game is different - they are full of confidence, they have nothing to lose, they are a team with no pressure.
"For them to lose 3-0 or 5-0 is exactly the same so after the 3-1 they come to the game and we were a few minutes where we should be smoking cigars and then suddenly everything is in trouble."
Watford boss Marco Silva was disappointed Rojo did not receive a second yellow card for the challenge on Pereyra that resulted in the penalty, suggesting United would have not have been able to stymie their comeback with a man fewer.
"In the second half it was clearly a second yellow for Marcos Rojo with the penalty, and then everything would have been different because it would have been 3-1 and they are down to 10 men," Silva told the BBC.
"I'm sure it would have been very difficult for them if they were down to 10 men.
"We have to keep going. The result is hard to take for us, we didn't deserve this result. In the end the quality was the difference, the individual players, but of course, the budgets of the clubs are so different.
"Now it's the moment to rest our players and to analyse what we will do to compete again and show our fans what we can do."