The 47-year-old was appointed as United boss on Thursday, less than a month after being axed by Derby.
Clough has said that the dismissal took him and his coaching staff by surprise.
"It was fairly shocking, yes," Clubcall.com quotes Clough as saying.
"I don't think we're over it, that's why this will certainly help in that way. We gave five years of extremely hard work, but I think it also helped in coming back in straight away.
"I certainly think we can use it in the short-term as additional motivation. I think we're reasonably motivated as it is, but in the short-term we'll certainly be using it. There's certain feelings that are still there that we'll try and keep beneath the surface for as long as we can."