Allardyce was heavily criticised in the winter for West Ham's poor form, but an impressive run has seen the team climb to 11th in the Premier League with six games remaining in their campaign.
"You have to admire the board for sticking with Sam," Nolan told The Guardian. "We had a very tough time early in the season with injuries.
"I don't think I've ever been through a season where so many major players have been out. At one stage we had all three of our central defenders out but our aim now is to finish in a top-10 spot.
"I'm sure if we'd had our squad for the full season we would have had a better season. We wouldn't have been in and around the relegation zone. We wouldn't have been talking about relegation."
The Hammers host title chasers Liverpool at Upton Park on Sunday afternoon.