However, the usually stoic Scot was visibly moved by the reception he received both before, during and after the 2-0 win over West Ham in his final appearance at the ground he has called home for 11 years.
Moyes said he was "gobsmacked" by the whole day and from the moment he arrived at the ground and was applauded in by stewards he did not quite know how to handle things.
Misplaced fears fans would show their displeasure at the manager allowing his contract to expire in order to succeed Sir Alex Ferguson were dispelled the moment he appeared on the touchline to loud cheers.
But Moyes said he could understand if some supporters, who sang his name throughout, were not happy with his departure.
"I am a football supporter and if I had been on the terraces today [Sunday] I would have clapped the manager - I might not have liked what he was doing but I would have certainly applauded," said the Scot, who was given a guard of honour by his own players prior to the post-match lap of appreciation and was visibly moved.
"I think just by the reaction from most people in the last few days I thought it would be okay but if you are a football supporter you are entitled to support your team and if someone is not on your team you don't know what will be the reaction.
"It was really emotional from the moment I came in: all the stewards were standing clapping me and I didn't know what to do.
"I came here 11 years ago and it was really emotional walking out on to the pitch, a lot of people didn't know who I was I don't think.
"I got off to a great start (winning 2-1 over Fulham) so I am really fortunate I had a reception like I did today [Sunday].
"I am gobsmacked, very thankful and humble for what the people of Everton have shown today.
"What I will miss is what you saw in the middle of the second half - the supporters were not cheering David Moyes, they were cheering their football club and standing up for it.
"I thought that was the toughest part for me today [Sunday] - it was a difficult time - because the crowd showed how big Everton are and what it means to them."
Goals from Kevin Mirallas after six - from a slick passing move - and 60 minutes wrapped up a comfortable victory.
Moyes felt his side displayed their true quality and certain passages of play would have been welcomed by his new employers down the M62.
"More important for me was how well Everton played today," added the Toffees boss, who was applauded out of his final press conference at Goodison by the assembled media.
"I thought they played like a top team today - I don't mean a team in fifth or sixth, I mean a top team.
"I think we would have been a match for any side: the players were terrific in showing a level of professionalism just to make sure they couldn't get caught up in anything."
West Ham boss Sam Allardyce felt his players buckled under the significance of the occasion for the home side.
"The way we played today we were lucky to get away with 2-0," he said.
"There was only one player who has been outstanding for us and that was (goalkeeper) Jussi Jaaskelainen who made some outstanding saves.
"I warned the players before the game what it was going to be like - it was exactly that and the players couldn't cope."