The Belgian missed a number of chances to complete his hat-trick too, while Paul Pogba also saw a penalty saved, but Lukaku was nonetheless pleased with his side's improvement in front of goal.
"That was really big. In the last game we started well but didn't take our chances. This time we did," he told BBC Sport.
"We knew we had to grind out the result in the second half. We have character and we need to be more like that. The last game against Tottenham - we were disappointed. Today we did score and we have to keep winning to try and catch the teams above us.
"Now we go into the international break and can switch off a bit. The manager has time to analyse our performances for the rest of the games in September."
Lukaku's brace was his first since scoring twice on his debut for the club at the start of last season.