A brace from Wayne Rooney and Juan Mata's goal put United in a commanding position before Roma hit back with two unanswered goals of their own in the second half at Sports Authority Field.
It was United's second consecutive win in their pre-season tour of the United States and the Premier League side's first in the International Champions Cup.
Van Gaal was still critical of United's display, though he did concede the heat played a big factor as his team faltered after the break, despite regular drinks breaks.
"I am pleased that we have won but it was not a good performance," said the Dutchman, who lamented the kick-off time during his pre-game conference.
"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 today.
"I said when the World Cup was here in '94 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."
While he was disappointed with the state of play, the Dutchman was impressed by the standard of goals on show, from both teams.
Rooney got the ball rolling with a curling effort from outside the penalty area, while Roma midfielder Miralem Pjanic delighted the crowd after catching goalkeeper Ben Amos off his line and scoring from inside his own half - similar to David Beckham's stunning strike against Wimbledon in 1996.
"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," he added.
"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."
