Many have put the Hammers' success last season down to the absence of supporters at the often hostile London Stadium, feeling that players could perform without pressure.
West Ham had the second best home record in the Premier League last term, with only Manchester City bettering them, playing just two games in front of a very small amount of supporters.
Monday's meeting with Leicester will be the first game at a full London Stadium since a 3-1 win over Southampton in February 2020.
When it was suggested to Moyes that his side might have played better with empty stands and asked whether he had any concerns over the impact of their return, he said fans will want to make a point.
"If I am a West Ham supporter, I am taking that as criticism and I am going to prove to you that the team will thrive and that we do support the team," said Moyes.
"It is going to be interesting. We played very well last year during lockdown. I believe we will continue to play well with the crowd or without the crowd, whatever we get. I think the crowd can make a big difference. We’ve got 60,000 back at the stadium and I am expecting them to get right behind the team and show their support."
Fans would have been hopeful of seeing a new signing line up against Leicester but the Hammers are very unlikely to add any new faces before Monday.
Moyes and co-owner David Sullivan continue negotiations over a deal for Chelsea's Kurt Zouma, though his wage demands of £125,000-a-week are proving problematic.
“I do [think we’ll see some business],” said Moyes. “I hope to do some more business. We have been trying hard and we are trying to add to a good group of players. We have a challenging season ahead of us and I am hoping we can do something but we have no guarantees."
After West Ham coach Stuart Pearce opened the door to a return for Jesse Lingard on national radio earlier in the week, Moyes said there would be interest in the England international should he look to leave Manchester United before the August 31 deadline.
"Pearcey is a great spokesperson, don't worry about that," said Moyes. "Of course we enjoyed having Jesse [on loan] but he is a Manchester United player. The questions are not for me but for Manchester United. If the opportunity arose for us to get Jesse, we'd be interested."
Lingard is currently training with Manchester United again having missed the opening day of the season following a positive Covid test and intends to remain at Old Trafford and fight for his place in Ole Gunnar Solskjaer’s team.