Media reports surfaced on Sunday concerning the future of the England international, who came off the bench in United's 2-0 loss at Everton.
However, in his post-match press conference at Goodison Park, Moyes ruled out talk of a possible close-season exit for Welbeck.
"Danny Welbeck is really important to me and I really value him," the Scot said.
"He's really important to Manchester United."
Sunday's defeat means United are certain to miss out on UEFA Champions League football next season, and Moyes paid tribute to the fans who have stuck with the team throughout a difficult campaign.
"The supporters have been incredibly behind the team and supported the team throughout," he added.
"They've realised it's been a difficult season and I think they've supported the team, but they understand it's not been good.
"I've recognised it's not been good and it needs to be better."
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