Danish striker Rasmus Hojlund scored an early brace to help Man United claim a fourth consecutive Premier League victory.
The 21-year-old opened the scoring inside 36 seconds to become the youngest player to score in six straight Premier League matches.
Hojlund quickly doubled the visitors' advantage, before Carlton Morris pulled a goal back in the 14th minute to give Luton a foothold.
As it proved, there were to be no further goals in the contest, as both teams missed chances to add to their respective tallies.
While Man United are unbeaten in seven competitive games, Ten Hag believes that his side can still improve upon their performance at Kenilworth Road.
Ten Hag told reporters: «Fragile [at times], because we didn't take the chances, I think we should have scored many more goals. After 2-0 there were big chances for Rashford and Garnacho, it could have been 3-0, 4-0.
»We dropped too deep and we allowed them some crosses and a lot of shots and some chances. After half-time they of course upped the pressure. We missed some really massive chances and we should of scored and we know that.
«On the other hand, Luton Town have lost games this season, but only two times by more than two, so it is not easy here. Apart from last week their performances and their results are very good.
»The way we started was perfect and that's the way we want to do it, it was a perfect game plan but the only thing we didn't do is be more clinical in front of goal. We must score more goals because today we could have easily scored five goals."
The Man United manager was full of praise for Hojlund, who has scored seven
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