Manchester United manager Jose Mourinho said he, his players and even the club's supporters will need to raise their game when arch rivals Liverpool visit Old Trafford this weekend.

United ground out a 2-0 win against Hull City in Tuesday's League Cup semi-final first leg and it took an 87th-minute header by substitute Marouane Fellaini to make the game safe.

United have now won nine games in succession, but with Liverpool five points above them in second place in the Premier League table, Mourinho wants everyone to be at their very best on Sunday.

"I was a bit disappointed with the first half," he said. "They were well organised defensively. It wasn't easy for us, but we were a bit sloppy.

"We complicated things; always one more touch, delaying the decision, giving them time to regroup. It was not our best first half.

"I think in the first half the players have to do better, I have to do better, the fans they also can do better. In the second half we all improved a little bit, just a little bit.

"I think now about Sunday. And Sunday I need to do better, the players they need to do better and the stadium they need to do better."

United captain Wayne Rooney went into the game against Hull needing one goal to set a new club scoring record, having equalled Bobby Charlton's tally of 249 in Saturday's 4-0 FA Cup win over Reading.

His moment appeared to have arrived six minutes into the second half when he was picked out by Paul Pogba's glorious pass, but he rattled his shot wide of the left-hand upright.

Juan Mata broke the deadlock five minutes later, ghosting in to volley home from close range after Henrikh Mkhitaryan had headed Antonio Valencia's cross from the right back across goal.

Pogba left the post quivering with a free-kick before Fellaini netted a potentially pivotal goal with a header from Matteo Darmian's in-swinging cross.

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The Belgian midfielder had been booed by his own fans prior to coming on in United's 1-0 win over Tottenham Hotspur a month ago and he celebrated his goal by bear-hugging Mourinho on the touchline.

"I think he wanted to show that he knows how much I supported him in a couple of difficult moments for him," Mourinho told Sky Sports.

"It was probably because I told him he'd score the second goal. It was nice for him to score the second goal in front of the fans and a second goal that can be an important goal."

United were missing 18-goal top Zlatan Ibrahimovic due to illness, but Mourinho said he expected the Swedish striker to be fit to face Liverpool.

Fellaini's goal was a body blow for Hull, who welcome United to the KCOM Stadium in the second leg on January 26.

Hull manager Marco Silva was only able to name six substitutes due to injuries and saw both Markus Henriksen and Josh Tymon hobble off during the course of the game.

Asked if Hull could still turn the tie around, the Portuguese replied: "We'll see, we'll try. It's an obligation always to try to do better and continue with our dream.

"Our dream is to play this final. It's difficult, but when it's time to play we'll compete."

Hull are reported to have turned down an offer from West Ham United for their set-piece specialist Robert Snodgrass.

Silva said he was unaware of any developments regarding the Scotland international, but with his squad so thin, his priority in the January transfer window is to buy rather than sell.

"In this moment we don't want to sell important players," he said. "We need to improve our roster with quality players."