Throughout United's pre-season tour of America, players such as Juan Mata have spoken about their respect for their new boss and the impact the Dutchman is already having.
"We’re all trying to impress him, whether it’s in training or around the hotel, with the way we conduct ourselves,” said 24-year-old Smalling.
“He’s a man who requires a lot of respect and we give him that because of what he’s done and what he’s like.
“Whether it’s the form, what we eat, when we rest - he’s really got the whole overview. He’s definitely got all that in hand. He’s a man that we can learn a lot from.”
Van Gaal has scrapped the team's traditional 4-4-2 formation and replaced it with a new 5-3-2 strategy, which was something Spanish midfielder Mata claimed he felt he would benefit from.
Smalling says it has been a big change, but he also thinks he could thrive under it.
“We’re picking it up, there’s obviously a lot to learn but we’re enjoying it,” he added. “It’s a lot of responsibility to go out there and attack the centre-half. He wants us to go aggressive and I think that’s my game so I’m looking forward to it.
“There’s good communication all amongst us. We obviously have to shift across and work into the space, so communication is massive and we get on well, so that’s not really an issue.”
United delivered a 7-0 pounding to LA Galaxy on Thursday, followed up by a tougher 3-2 win over Roma on Saturday.
Wayne Rooney scored two goals in both games and Smalling says Rooney’s skill is going to be invaluable.
“Four goals in two games, that’s what special players can do,” he said. “Rooney turns there and you think he’s got nowhere to go but he puts it in the top corner. That’s that class that we’re going to need this year."
Van Gaal will lead United into their first 2014/15 league game on August 16 at home to Swansea City.