United entered the clash with Burnley off the back of successive Premier League defeats to Brighton & Hove Albion and Tottenham Hotspur.
However, a double from Lukaku saw the Red Devils return to winning ways ahead of the international break.
"In the first half we showed a lot of quality and in the second half we showed a lot of character and mentality," Lukaku told MUTV. "We have the mentality, but it needs to come out a bit more.
"That is what the manager wants and that is what we need to do. We needed the win, especially after back-to-back losses when we conceded three goals, which didn't happen last season. We are delighted with the win and we have to move on from this.
"We are Manchester United, this is how we have to play in every game and against Tottenham we did the same. The people will now see a different side of us. Everything that we worked on in the last couple of weeks is coming out now - lots of quick passing, runs in behind, a lot of action and a lot of chances.
"As long as we create chances, we know we will score. We defended well, we tried to press the ball, the fans want to see that and we tried to deliver."
United will return to action with a trip to Watford after the international break.