Hammers midfielder Manuel Lanzini has apologised and made a donation to an east London foodbank after breaching the rules over the Christmas period.
Britain on Friday reported a record 1,325 deaths over a 24-hour period from people testing positive for Covid-19 as overstretched health services struggled to cope.
Moyes acknowledged Argentina’s Lanzini made a “mistake” but insisted the vast majority of players were abiding by the game’s strict protocols.
Asked if sterner action needed to be taken against offenders to ensure compliance after a series of incidents involving high-profile footballers, Moyes pleaded for equal treatment.
“If you are going to take tough measures on players, then you might as well take them on the government people as well who have broken the rules because it’s certainly not just football players who have done it,” he said.
“We’ve just got to be careful that everybody isn’t picking on football players.
“A lot of people are throwing stones in glass houses at the moment regarding this. We all know what the protocols are, we all know we have to be ever-vigilant and make sure we’re doing the right things.
“But we can all make mistakes as well. Manuel Lanzini understood he made a mistake, he has apologised for it, he’s made a donation to the foodbanks for what he’s done and I think it was a really good gesture.”
Moyes’ comments came a day after Newcastle head coach Steve Bruce questioned the morality of football continuing during the pandemic.
The Scot, however, believes sport is playing an important role and saluted the players for their contribution.
He said: “We have to remember that the players are the ones taking risks every week. They continue playing, they have to go back to their families, so we have to say that the players are the ones out there who are taking a lot of risks.”