Fellaini, making only his second start in the league since January, was one of United's better performers but after an eighth home draw of the season, he admitted United's home form has to improve.
The Manchester United manager revealed his frustrations at another team coming to Old Trafford with the sole intention of getting a point and defending the box and not showing any ambition to try to play football against his side. "There are nine games to play and we have to think step by step and at the end if we deserve to win the title I will be very happy". We have moments or periods when we push but then a couple of players disappear for 10 minutes, when you don't see them.
United last lost a league game in October when they were humbled 4-0 by Chelsea at Stamford Bridge, and Mourinho is enjoying his longest unbeaten run in the top flight since October 2005 when his own Chelsea side went 40 games without defeat.
Everton visits Old Trafford on Tuesday with United having top scorer Zlatan Ibrahimovic and midfielder Ander Herrara available again after suspension.
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Tuesday's game comes too soon for Morgan Schneiderlin, and Aaron Lennon, James McCarthy, Ramiro Funes Mori and Seamus Coleman are also injured.
Paul Pogba remains a doubt with a hamstring injury, while Juan Mata, Phil Jones and Chris Smalling are out. "We've had matches here with Zlatan that we drew", said Mourinho.
"I'd be looking at that situation thinking that on Saturday (Mourinho) played Ashley Young at left-back, that he has been playing Matteo Darmian at left-back, Marcos Rojo, Daley Blind".
But Pulis, speaking after the game, was quick to insist that United, under Mourinho's tutelage, will challenge for the title next season.
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Ronald Koeman is vying to become the first manager in Premier League history to win three consecutive away games at Old Trafford.
"I can not compare the way he trains, the we he commits, the focus, the ambition".
"He's said some harsh things about a few players this season at time Jose Mourinho and others have responded..."
In November, he was criticised by Mourinho for missing the Premier League win over Swansea after he said he was not able to play.
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His side fell behind in the fifth minute when Eden Hazard crossed from the left for Fabregas to score at the near post. But four minutes later, Palace scored twice in quick succession to leave Antonio Conte's men gasping for air.