The manager's exit was confirmed on Tuesday morning after being widely reported on Monday and the former Everton boss has since spoken of his pride at being asked to lead the Red Devils.
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"We do not accept that it was handled in an unprofessional manner," a Manchester United spokesman told Press Association Sport.
"The decision was not taken until late Monday night and was communicated face-to-face first thing on Tuesday morning.
"When reports started emerging on internet news sites on Monday afternoon, no decision had been taken at that time."
Ryan Giggs has subsequently been appointed interim manager at Old Trafford and Goal understands that the club's owners, the Glazer family, are due at Carrington on Friday to discuss who should succed the Scot.