Rumours have circulated that the Hammers are to dispense with Allardyce due to the supporters' dislike of a his direct style of play.
But Nolan, who came to prominence under Allardyce at Bolton, believes West Ham are fortunate to have their manager.
"It's been one of those seasons but it's great to know that we'll be back in the top flight next year, which has been the gaffer's main priority," he told the club's website.
"Now that we know we are going to be in the Premier League I'm convinced that there's only one way that we're going to go and that's to get better and better as the years go on.
"This year's been really difficult with injuries, obviously a few suspensions as well along the way, but it's nice to be able to put this season to bed now and look forward to next season.
"I really think that given the backing in the post season and then pre-season that we can push on next year and do the business.
"If we didn't have the squad we have, or the lads we've got here then I don't think we'd have survived and I don't think many other teams would have survived with everything that's been thrown at us.
"It's credit to the gaffer and all the boys for making sure that we are here now and for making sure that we're going to enjoy another great year in the Premier League next season.
"We're going to be a lot better and I'm sure that we'll be in and around that top 10."