Louis van Gaal was pleased to see Manchester United get three points on the board in Champions League Group B with their 2-1 win over Wolfsburg but stressed there is still plenty of room for improvement.
The result at Old Trafford saw United bounce back from the 2-1 loss to PSV Eindhoven they suffered in their pool opener, and was a fourth straight victory in all competitions for the Red Devils, who are top of the Barclays Premier League.
But it was not entirely convincing, with them having to come from behind after Daniel Caligiuri's fourth-minute strike and then, following Juan Mata's penalty and a Chris Smalling goal, hang on to their lead towards the end.
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United boss Van Gaal said: "We have to keep our feet on the ground and we have to improve a lot to be at the top of Europe.
"We have beaten Wolfsburg, I am very happy and the players are very happy, but we have to improve on the second-half performance and we have to know that, and I have said that also to the players.
"That is why we are here - to improve ourselves so we win every game.
"We could have won this game in a better way.
"However, I think we deserved to win because we created much more chances that Wolfsburg."
Van Gaal felt United got lucky when they were awarded the 34th-minute spot-kick for a handball by Caligiuri.
And the Dutchman suggested overall that United's team spirit had been a key factor in the win, while also claiming bad luck and tiredness had been to blame for some of their sloppy play.
"There are referees who are not whistling for such an incident so then you are lucky that he is whistling," Van Gaal said of the handball.
"But in the first half I was very pleased. We created so many chances - but then you don't finish them, and that is unlucky.
"Then in the second half we continued with our game spirit and made a beautiful goal.
"But after that it was not good anymore, which is remarkable because keeping possession is something we have done very well for the last five or six matches.
"We had given a lot in the first half, and also, (it is about) the accumulation of the matches in the last weeks because I cannot understand (otherwise) why we would give the ball away so easily.
"But I think also the team spirit still kept us in the match."
Mata won as well as scored the penalty and provided a delightful tee-up for Smalling's 53rd-minute sliding finish in an eye-catching performance by the forward.
But when asked about Mata's display, Van Gaal said: "I don't speak about individual performances but I have seen Mata playing better than today.
"I can say as a manager he played very well and I agree with you - but I don't agree with you."
Van Gaal also emphasised it had been his call that Mata would take the penalty over Wayne Rooney, adding as he said he had spoken to the latter about it: "I communicate always with my players - but I make the decisions."
The manager did have praise for Smalling, saying: "I think he played a very good match, especially defensively, and the way he scored a goal was outstanding."
Meanwhile, Wolfsburg boss Dieter Hecking had some strong words as he gave his analysis of the game, which he thought United should have finished with 10 men.
"I think it was a penalty but that we were unlucky there," Hecking said.
"And I thought the second goal was unlucky - as we say in Germany, a 's*** goal' - but then we were on top again and really could and perhaps should have scored again.
"In the 84th minute there was a foul on Julian Draxler that really should have been another yellow card (for Morgan Schneiderlin), so once again we just lacked that bit of luck at the end. But I'm optimistic we can build on this strong performance."