United were two goals to the good at half-time thanks to Lukaku's opener and Chris Smalling's resounding second, but allowed Watford back into the game after the interval.
Andre Gray set up a tense finish with a goal in the 65th minute, but Jose Mourinho's side held firm to record a second consecutive Premier League win.
Lukaku, though, was not impressed with his side's second-half display and wants an improvement in the coming weeks.
"Our quality made the difference in first half, in the second we were too sloppy," he told BT Sport.
"We were dominant. Chris scored and we had to try get the third, but as I said we were too sloppy, and we will watch the images and improve on that."
Mourinho singled out the Belgian after the game, citing his work ethic as the benchmark that every other player in his side should aspire to.
"His tackle after a 70-metre run in the right-back position says everything about what I want from my team," the Portuguese said.
"I want to play like in the first half, then when in trouble you need to resist the trouble, and you only do that if you're a team and we were."