"This level will be no problem for him because he is a level-headed man who understands the massive jump between the Championship and Premier League," said Grant, who has become an important part of Albion's backroom staff since moving to The Hawthorns during the summer.
"Hopefully I can help with that because he has never been there before as a manager and I have been there on the coal face on the coaching side recently. We want to compete in the league and I think we can do more than that.
"We will work hard on the training pitch to make sure we get the success that the club is striving for and Tony, the staff and the players want. I'm sure we can have a very good team."
Grant claims Mowbray is already looking ahead to the future, not least January's transfer window.
"There has been a massive change in the Premier League even in the last four or five years," added Grant. "The biggest thing Tony has to manage is the transfer windows.
"In the Championship you can bring somebody in on loan any time and now we have to do it all at one time. A player who might have cost you £1million will cost you £6million because you are a Premier League club.
"I'm sure Tony will be glad that the window is closed so he can look at something else. And I'm sure he will already be looking at January but I has got a bit of time to do it.
"He is very good in that respect in that he won't be taking his eye off what is happening elsewhere. But he will be able to concentrate on the team."