That means the pressure is back on Chelsea, who host Manchester City at Stamford Bridge on Thursday evening, to close the gap between the fourth and the chasing pack.
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The Blues have 51 points with tonight’s game in hand, while United and Wolves breathe the neck with 49 points.
Solskjaer, however, looks beyond Chelsea and aims to dethrone Leicester, who have held third place for most of the season.
“I never said that the fourth was our goal, we want to go to the third but we have to focus on each game as we go along and there are also two cups for us there”, said Solskjaer told the Telegraph. “One game at a time and at the end we can count the points and maybe only have two teams ahead of you.
“Sometimes it was very, very good football. For me, we could and should have scored more goals and put the game to bed before half time.
“It is worrisome when you go at half time knowing that you should score two or three more goals, but the control and the way we supported and prevented Sheffield United from playing was also very good.
“I am very satisfied with the performance but there is still more to come. We should not be 100% satisfied. “