Following Saturday’s goalless draw with Leeds at the Amex Stadium there was booing from some of the home support as the Seagulls saw their winless run in the Premier League extended to eight matches.
Boss Potter was left “a little bit perplexed” by the negative reaction, later suggesting those fans who did vent their frustrations could have found themselves somewhat caught up in the moment.
Brighton head to the London Stadium on Wednesday night sitting ninth in the table.
Moyes believes Potter deserves full credit for the way he has continued to move the club forwards.
“They are really lucky to have Graham Potter as manager and you shouldn’t forget that,” said Moyes. “He is a top manager, has got a really good team.
“We all get booed at times in our career. You just have to move on and I’m sure Graham knows what he is doing more than the people who booed.”
Moyes added: “Every team who plays Brighton understands that they can cause you problems, play with a really good style and have made a good start to the season.
“I think Graham Potter has done a really good job. They have gone about their work really well. If you asked me last season who I would tip to improve, I would say Brighton.
“I think overall they are a well-run football club and Graham is a really good manager.”
West Ham will be looking for a response following successive league defeats after losing at Manchester City on Sunday.
Moyes’ side head into the midweek games still in fourth but now ahead of Arsenal only on goal difference and with Wolves just three points behind.
“The way we have been playing has given this huge belief and I don’t think not winning at Man City would necessarily give us a huge dent,” said Moyes, who hopes to have defender Aaron Cresswell available after overcoming a back issue.
“Overall I do think that we want to get back on it. We want to get back winning.
“If we are going to be competitive – and continue to be competitive – then we have to pick up points and it doesn’t matter where it is.
“I wanted us to compete against the big teams, but competing also means winning games as well.
“We competed really well against Liverpool at home a few weeks ago and beat them. We competed well against Man City but we couldn’t get a result against them.
“That will happen in games because we are just not quite at that level yet, but we want to try and keep pushing for it.”
Moyes feels there is very much a different vibe around the London Stadium as the Irons look to continue their progress, which has seen them already qualify for the knockout stages of the Europa League.
“Having three (successive) home games now, we will hopefully try and use it to an advantage,” said Moyes, whose side host Chelsea next weekend ahead of the visit of Dinamo Zagreb.
“The crowds have been brilliant in the stadium and we need them all the time.”
Uefa, meanwhile, confirmed West Ham’s appeal against a fine for crowd trouble during their 2-0 Group H win over Rapid Vienna on September 28 had been partially upheld.
The original sanction of a 60,000 euro (£50,500) penalty has been amended to 30,000 euro (£25,500) for “throwing of objects”.
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