Ten Hag officially took charge of the Red Devils at the end of last month, with pre-season training beginning on June 27, while he has now had two games at the helm.
The 20-time English champions opened their pre-season with a 4-0 win over Liverpool on Tuesday before recording a 4-1 victory over Melbourne Victory in their second fixture on Friday.
McTominay played the opening 45 minutes in both of the pre-season friendlies, and the Scotland international is expected to be a regular for the club again next term.
The 25-year-old has said that there is "a lot" to take on under a new manager, but he is enjoying the fresh approach that the Dutchman has brought to the club.
"Whenever you've got a new manager, there's a lot of new ideas, a lot of things we have to take on board in terms of what the manager wants from us, a slightly different formation as well and different ideas, which is important," McTominay told MUTV.
"We need to dial into them, and I think tonight is a good test in terms of the team that we're playing against. They played a little bit deeper, it's harder to break down, [so we have to come up with] different ideas and ways that we can get into their box and create scoring opportunities.
"Everyone's so, so happy with the new coach in terms of the detail and attention to the work that we're doing, and everyone's so fit now. And we can get fitter, I can get fitter, the whole team can, which is obviously a benefit for the future as well."
McTominay has also said that Friday's pre-season clash with Melbourne Victory acted as valuable preparation for the start of competitive action next month.
"They were very organised in terms of the two blocks they had; they were difficult to get through in the middle of the pitch," he added.
"We had quite a lot of bodies between the lines and that forced us to go to the sides. I think that's the best way to break teams down when they play a five [in defence].
"The manager said that at half-time. We kept patience, we didn't panic, in terms of going 1-0 down. There's things we can improve on and we're looking forward to it as well."
The Scot was again an important player for Man United during the 2021-22 campaign, making 37 appearances in all competitions, contributing two goals and one assist in the process.
McTominay will face competition for a starting role next term, though, as Christian Eriksen has arrived to boost the midfield, while the club continue to chase Frenkie de Jong from Barcelona.
Man United are also said to be on the verge of signing Lisandro Martinez from Ajax, and there have been suggestions that the Argentina international could be used as a holding midfielder.