Moyes knows there's anger about his interest in Leighton Baines.
"I'd never be surprised by football supporters, but I think Everton's are well aware of what was done at their club," said the United manager.
"The Premier League has been going just over 20 years, and they had a top 10 finish maybe once in the first 10-year period. In the second, we finished in the top 10 on a regular basis. I think if someone really looked at it, they would understand and hopefully realise that I helped push the club in the right direction.
"But I would not be surprised (if there was some flak). I had a great rapport with the fans at Everton, but things would not surprise me, because I have got to do a job for Manchester United, while they have to support their team, which they have always done.
"We were not happy when we lost Joleon Lescott to Manchester City, so I totally understand (anger over the Baines bids) and have no qualms about it at all. That is football, and if it happens, it happens."
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