A Wayne Rooney double and a chipped finish by Juan Mata had United cruising at 3-0 at the break in stifling conditions in Denver, but a stunning long-range strike from substitute Miralem Pjanic and a late Francesco Totti penalty left Van Gaal's men struggling in the closing stages.
They held on though as the Dutch boss recorded his second successive win since taking the reins at Old Trafford and saw his side continue their form on their American tour in the International Champions Cup.
It was quite a contrast from United's 7-0 demolition of LA Galaxy last week and although their flowing football was affected by 10 changes made for the second half, Van Gaal was unhappy with his team's stuttering showing, as well as the scheduling of the fixture in such hot conditions.
"I am pleased that we have won but it was not a good performance," the 62-year-old told the club website. "Over 54,000 people came to watch us but we can perform much better.
"We are not used to this hot weather. I think we didn't play a good match because of the height of the stadium, the air, because all my good passers failed. I said when the World Cup was here in 1994 it wasn't wise to play here at noon. America has a top sports climate but you have to play football at the right time.
"When you are 3-0 ahead, the only thing you have to do is keep the ball in possession and then the opponent has to run and run and run. It’s very difficult in this hot weather to do that.
"But we forgot to do that [keep possession] and we brought Roma into the game ourselves."
With midfielder Tom Cleverley chosen to skipper the team, Rooney impressed in front of goal again with his fourth goal in two games on American soil.
The striker's opener was a fabulous curled strike from outside the box and Van Gaal added: "Some of our passes failed, the ball was bobbling all the time and we didn’t create so much, but we scored three fantastic goals.
"The pass from Rooney to Mata was unbelievable, despite the heat and the height. Mata was running with his brain at the right moment.
"They also scored one fantastic goal, so then it was 3-1. But the penalty was not right: you cannot award a penalty when a shot hits your hand or arm from two metres away."
United will next play Inter Milan on Wednesday and will come up against former centre-half Nemanja Vidic.