Phillips was involved in a heated exchange with supporters on Saturday following the 4-3 Premier League defeat to Newcastle.
The 28-year-old England international was pictured making a middle-finger gesture towards fans who had criticised him as he boarded the team bus.
Moyes, however, refused to condemn Phillips' actions and urged the London Stadium crowd to get behind the player ahead of Tuesday's Premier League encounter at home to capital rivals Tottenham Hotspur.
"Kalvin's a human being and can do things which we all do at difficult times," said Moyes.
"What he needs is support behind him, people to help him and we're going to stand with him and help him as much as we possibly can. Obviously, we need all our supporters to give all our players, whoever it is, their support."
West Ham had been leading 3-1 at St James' Park when Phillips was sent on as a substitute with 21 minutes remaining.
Phillips, however, gave away a disputed penalty by inadvertently kicking the leg of Anthony Gordon while trying to clear the ball and was also beaten comfortably by Harvey Barnes before he hit Newcastle's last-gasp winner.
Phillips had previously been responsible for conceding goals in his first two matches since joining on loan from champions Manchester City in January and was needlessly sent off in his fourth, at Nottingham Forest.
The former Leeds favourite was substituted at half-time on his last start -- when West Ham were 2-0 down at home to Burnley -- and subsequently lost his place in the England squad.
Phillips is set to be on the bench again for the match with Spurs and Moyes was adamant he could yet transform the move into a successful loan spell.
"He's fine, he's back training and we've all moved on from the weekend," said Scottish manager Moyes. "We've got a big game coming up and we're getting ready for that now.
"Kalvin Phillips is a really good player, an international player and I do believe he is an excellent footballer. And I do believe we can still make something out of the time we've got left with him here."
