Allardyce's side conceded four goals in 10 minutes as the Gunners ran riot in the second half to extend the Hammers' winless run to five matches.
"It was totally unacceptable for us with the standards we have set ourselves," Nolan told the club's official website. "The gaffer wasn't happy and rightly so - so he asked for us to come in at 7am the next morning on the Thursday.
"There were no complaints from any of us - we all need a kick up the backside every now and then and we take it all on board.
"The gaffer and all of us wanted to put this result and what happened to bed straight away, and it was good that we came in early and got into looking at what went wrong together as a group."
Midfielder Mohamed Diame, who joined West Ham last summer from Wigan but has been linked with a move away from the club this transfer window, was late for the meeting.
Nolan added: "We all had to wait for him before we could start and when he arrived, we all gave him stick for not only being late and keeping us all waiting, but we said we thought he had left us without saying goodbye."
West Ham's next game is away at Fulham in the Premier League on Wednesday 30 January.