Crystal Palace manager Patrick Vieira conceded the late equaliser was “brutal” on his team.
The French forward scored in the fifth minute of added time to cancel out Wilfried Zaha’s first-half penalty, which was his eighth goal against the Seagulls on his 400th appearance for the south Londoners.
Maupay had the last laugh when he lobbed the ball over Vicente Guaita in scenes reminiscent of the Eagles’ win at the Amex in February where Christian Benteke had netted deep into stoppage time.
“When we played Palace at home we were the better team but lost 2-1,” Potter reflected.
“The feeling is considerably better this time. It is a wonderful feeling for us now, to celebrate in front of our own support, a 96th-minute goal, when the scoreline was 1-0.
“I am happy for the players, they kept going in a tight game which had nothing in it. I thought it was fairly even.”
A win for Brighton would have sent them to the summit of England’s top flight for the first time in their history but they were largely second best.
Palace had enjoyed the better of the first half and deservedly went in ahead after Leandro Trossard brought down the impressive Conor Gallagher in the area and Zaha stepped up – instead of usual taker captain Luka Milivojevic – to score once more versus the south coast outfit.
Jordan Ayew could have put the game to bed with 14 minutes left when Benteke put the Ghanaian through but he side-footed wide to extend his goal drought to 35 matches, before the Seagulls provided a sucker-punch.
Potter added: “It’s not something we think too much about, the league table after six games, but we have won 13 points so we have more than two points a game.
“And we know we can still improve. Performance-wise we can be better but we have kept going and got another point.”
Patrick Vieira was left frustrated that his side could not close out what would have been a second win of the campaign.
“This is the word – brutal, because we had a good game,” the new Eagles boss said.
“It was a really challenging game, playing against a good team but we scored before half-time and in the second half they didn’t create many chances.
“We had the chance to score the second goal, didn’t take it and then we conceded at the end. It is brutal and I am really disappointed for the players because they worked hard to get the win.”
There were ugly scenes after Maupay’s dramatic equaliser which sparked wild celebrations among the away supporters but Brighton captain Lewis Dunk cupped his ears to the home faithful.
Palace midfielder James McArthur and Seagulls goalkeeper Robert Sanchez clashed at full-time while the Eagles fans gave Dunk a volley of abuse as he left the pitch.
Maupay and Zaha also exchanged words as tempers boiled over in a match which saw six yellow cards handed out.
But Vieira insisted: “This is the derby and in derbies there is a passion, teasing fans and players, this is part of the derby and one of the reasons we all love these games.
“When it is not going over this limit, this is something we all accept.”