Andy Carroll was fined following what Moyes described as the striker's "unacceptable" and "inexcusable" behaviour against Manchester City last weekend and was then sent home from training for refusing to apologise.
"The first half performance was excellent, at times it was as well as we've played", Moyes told BBC Sport. What matters most is that Leicester look set to end the season inside the top-half, providing them with a good platform to build off heading into the next campaign.
"We knew before the game that it was crucial that we got three points".
"I think everyone was aware of the importance of the game, three of them to go, the sooner we got a win the better and I thought the players went about it in the right way today".
Whilst he has struggled to adapt to life in England, if given the platform from which to play regularly at West Ham, he could prove to be a really shrewd signing for the Hammers.
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His cause was not helped on Saturday by the absence of nine players through injury and suspension but Leicester's performance, on a hot afternoon, was lukewarm at best.
He said: "The game was a big disappointment". I couldn't care less who scores as long as we get the points.
"All we can do is have a good week in training and put all our focus on our next game".
"If we can finish strongly that will be encouraging and important for the next season".
"The team is more than capable of winning lots of games".