Potter's father had passed away shortly before the fixture and Moyes offered the Albion head coach words of comfort on the touchline ahead of the Premier League match.
Potter's Brighton will meet Moyes' West Ham once again this Saturday at the Amex Stadium and the Albion boss said he will always have the utmost respect for the former Everton and Man United manager.
"I don't know David that well at all, just from brief conversations on the side," said Potter.
"But from the outside, I'm full of respect for him and how he has dealt with the challenges football has thrown up, he has always conducted himself with incredible integrity and professionalism.
"The way he has turned West Ham around is there for all to see, they have invested a lot over a few windows but haven't quite got the team, you could say. Now you can see that and that is credit to David and his staff.
"I will always remember he came over to see me when my father passed away when we played them last year, that was a nice touch - he didn't have to do that but it just showed the type of person he is and I have got huge respect and admiration for him."
Brighton secured their Premier League safety earlier this week but they have three matches of the season remianing, starting with West Ham who are fifth and chasing European football.
"The higher up (we finish) the better for us," said Potter. "We’ve achieved our base goal which is to make sure we stay in the Premier League.
"We need to improve on what we have done and make sure we’re here again next year, then we want to finish off with as many points as we can.
"The boys are ambitious, so we will try. We have got three teams coming up that are really strong, but that’s the beauty of it, we need to compete against them and do our best.
"West Ham have invested a lot of money over a period of time.
"It is credit to David that he has stabilised things last year and then improved again with a talented group of players.
"It is football so anything is possible but this year we try to focus on trying to finish this season off, having a break and recovery and then going again and trying to improve – that is the key."