Goalkeeper Heurelho Gomes denied Ibrahimovic with a magnifient diving save and then Watford manager Walter Mazzarri trumped Mourinho with his own substitute.
Colombian Juan Camilo Zuniga restored the lead with only his second touch only one minute after joining the game. Then, in stoppage time, Zuniga was tripped by Marouane Fellaini for a penalty which Troy Deeney converted.
United were joint leaders after three wins in their first three games. Then they lost 2-1 at home last weekend to Manchester City and that defeat appeared to destroy their fragile, newly-built confidence. A midweek Europa League by Feyenoord in Rotterdam followed.
Pogba exerted little influence on the match and both he and captain Wayne Rooney, who had another poor game, were booked for losing their temper under pressure. The sight of both players giving away possession much too often which would have frustrated still out-of-favour Bastian Schweinsteiger and Michael Carrick.
Mourinho complained that the first Watford goal was questionable because of a foul which referee Michael Oliver missed.
But he added: “In the first half we didn’t play well. In the second half we were much better. We got the draw and we were ‘the team’ then Gomes makes a phenomenal save and their second goal was down to our individual mistake.
“Luck will arrive when she thinks it’s the right moment but our individual and collective performances we have to improve.”
Mark Hughes is coming under heavy pressure as manager after Stoke remained fixed to the foot of the Premier League following a 4-1 defeat at Crystal Palace.
Palace were 2-0 up inside 12 minutes thanks to goals at set pieces from defenders James Tomkins and Scott Dann. Stoke improved after the break but nearly went 3-0 down when Bojan Krkic cleared a Dann header off the line.
James McArthur’s deflected strike was followed by a fine Andros Townsend goal before Marko Arnautovic scored a consolation with the game’s final play.
Claude Puel celebrated his first Premier win at fifth attempt as Southampton beat Swansea 1-0 at St Mary’s.
Nathan Redmond missed from 12 yards before a Charlie Austin strike hit the bar before substitute Austin chested down the ball and sent in a rising shot to put Saints ahead just past the hour.
Gylfi Sigurdsson had a late Swansea chance but saw his low shot saved.