While the 59-year-old has been criticised for his brand of football this season, Nolan believes that Allardyce can guide the Hammers into Europe in the coming years.
"Of course he's had a difficult week," the midfielder told the Daily Star. "With all the online stuff that goes on, it can go really stupid. But Sam's got a good rapport with the fans and I think they know that he knows what he's doing.
"If he's given the armoury he wants, he can build a team that will be challenging for Europe – and doing it the right way.
"You only have to look back at what we had at Bolton, when he was given the ammunition to go on and the situation he got us in."
West Ham return to Premier League action on Sunday when they entertain Liverpool in the league.