It was Ibrahimovic's 27th goal of the season and but for his contribution United would be a long way off qualification for next season's Champions League.
That result left United four points adrift of rivals Manchester City, who occupy fourth, but Carrick says Pep Guardiola's men can be caught.
The Swede has the option to remain at Old Trafford for one more season upon the expiration of his contract, but has given little indication as to his decision.
Manchester United's Jesse Lingard in action with Everton's Kevin Mirallas.
Mourinho declared himself pleased with Shaw's display, but warned the young full-back he has major improvements to make. With an assist from Ashley Williams, Jagielka pumped in the winning-goal to ensure that United suffered a major blow early in the English Premier League game.
Many of United's recent setbacks have stemmed from its failure to turn possession and clear-cut chances into goals, but this wasn't one of those occasions.
Zlatan Ibrahimovic has criticised Marouane Fellaini's mistake in Everton's opening goal.Читайте также: Project Scorpio reveal COUNTDOWN
But after Jagielka's defensive partner Ashley Williams was dismissed for handling Luke Shaw's drive deep in injury time, Zlatan Ibrahimovic stepped up to convert the penalty and ensure the points were shared. The clock had ticked into the 94th minute when Ibrahimovic slotted home the penalty.
"He had a good performance but it was his body with my brain", Mourinho said.
"I could feel some of the boys in trouble with the confidence levels". Things can't get any better for his Leicester counterpart, Craig Shakespeare.
The manner of their defeat meant Sunderland have now failed to score in their last five games and languish eight points from safety.
He injected a bit of spark, got down the wing several times and some [definitely not all] of his crosses were whipped into good areas.
United have won just once at home in the league in 2017, with the likes of West Brom, Bournemouth and Hull each taking a point away from the Theatre of Dreams since the turn of the year. There was misfortune, too, when Paul Pogba headed against the bar after the break before Ibrahimovic also had a headed goal ruled out for offside, with TV replays suggesting it had been the closest of calls.
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