Nolan has conceded that seeing Carlton Cole released was a surprise, with the club's pursuit of a replacement now Allardyce's main priority before the season begins.
He told the Evening Standard: "It could be another very good season for us. Big Sam has everything in place now. He can tinker with the squad, bring a few in, but all the time he is increasing the quality.
"Losing Carlton Cole, a big character in the dressing room, was a bit of a surprise but it was a decision the boss had to make. I know the club are working hard to get another striker in but the point is we trust the gaffer to do the right thing after what he has achieved here in such a short space of time. It was fantastic he signed a three-year contract in the summer.
"The gaffer has said he wants one more although it wouldn't surprise me if we sign a couple of players before the deadline, especially if someone decent becomes available late in the day. We have a good, settled squad but he will be looking to add more quality when he can. Big Sam isn't someone who will get a player in just for then sake of it."
Allardyce begins his second Premier League campaign with West Ham against Cardiff City on August 17.