The reigning Premier League champions were 2-1 winners at Sunderland at the Stadium of Light on Saturday after previously suffering back-to-back top-flight losses.
David Moyes’ men face Southampton at Old Trafford in their next fixture, and the Portugal international is confident the Red Devils will continue to improve.
“It was a very good win for us,” Nani told United’s website.
“We had a really good performance after being unlucky to lose a goal so early on. Phil Jones tried to block and it came off Vida [Nemanja Vidic] and just bounced for them.
“But I think we played very well in the second half and there was good shape from everyone. If we can get to our maximum for the next games, we will show the real Manchester United then.
“We knew it was always difficult to come to Sunderland to play but we’ve had some very good results in this stadium as well. We knew we had to play better than we did in the first half and we just had to find the right moments to come back.”
Nani also backed United youngster Adnan Januzaj to kick-on after scoring a brace at the Stadium of Light.
“It was a good day for him,” Nani added. “We know he has good skills and is a good player. He has chances to push on and I hope he can help us more in the team.”
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