Carrick wants United to build on Sociedad success
United, unusually, find themselves eight points adrift of leaders Arsenal heading into Saturday's match against Stoke at Old Trafford.
In their first season under new manager David Moyes following the retirement of Alex Ferguson, United have already suffered three defeats and two draws allied to just three wins in their opening eight league matches this term.
However, they continue to prosper in Europe though as they sit top of their group in the Champions League after Wednesday's 1-0 win over Spanish side Real Sociedad.
But consistent winning form has proved elusive for United, who last week could only manage a draw at home to Premier League surprise package Southampton.
England international Carrick, 32, urged United to start being ruthless in front of goal after they wasted a number of chances against the La Liga side in midweek having failed to see off Southampton.
"Of course our priority is climbing the league table," said Carrick.
"We haven't played too badly, especially against Southampton, but Saturday against Stoke is very important," he added.
"I thought we did more than enough to win the game against Sociedad, and should have won it by more.
"It would be nice to see some more go in to make it a bit more comfortable; it was a similar scenario last weekend against Southampton, so we were conscious of a goal in the last minute."
Moyes has come under criticism for United's poor start but Carrick believes they have time to force their way back up the table.
"I think we can improve on a lot of things, there's still a way to go until we're really at our best, but we haven't been playing that badly," said Carrick.
"Things haven't been going so well for us in terms of results, we'd love to score more goals, but the good thing is that we are creating the chances."
Robin van Persie, who missed the win over Real Sociedad with groin and toe problems, is expected to return against Mark Hughes' Stoke at Old Trafford.
"I hope he will be fit for the weekend," said Moyes when asked about the Dutch striker.
"He has had a couple of niggling injuries even before he went on international duty," the Scot added.
"They have all just caught up on him a bit so I thought if I had a chance to give him a breather I would do and fortunately for us it worked out fine."
Former United striker Hughes has not won as a manager at Old Trafford since 2006, when he was in charge of Blackburn Rovers, but the Welshman tried to put more pressure on Moyes by insisting the champions cannot afford any more slip-ups.
"You have to be careful," Hughes said. "There are only a certain amount of games you can lose. Five or six enables you to still be in the title race.
"Lose any more than six then you make it very difficult for yourself, nigh on impossible. They have already lost three at this stage. They can't afford any more slip-ups.
"Maybe they are a little bit vulnerable at the moment. But invariably when people question Manchester United they come back with the answers," added Hughes, who played under Ferguson.
"I don't think there's that aura around the club at the moment and maybe it's a good time to meet them."
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