"It is a big, big win for us, a much-needed win," said Maupay, who returned to the Seagulls side after starting on the bench against City on Wednesday.
"We have got quality we know that, but we need to keep pushing on and get more wins.
Manchester City manager Pep Guardiola told BBC Sport: "We knew how tough it would be. Brighton had a good mentality to play.
"We had a really good first half and had chances. After we missed a really clear chance in the second half, they were better.
Brighton head coach Graham Potter:
"It was tough for us at half-time of course because of the scoreline and how the half went.
"You're looking for a response, you're looking for character, and I thought we got it.
"In this period, we know how much we needed the wins," Arteta said.
"We had a really tough week and it wasn't that much about the performance, it was about the result.
"You need the results to start confidence and now with two wins, I think everyone is in a much better mood.
West Ham manager David Moyes told BBC Sport: "We saw a poor West Ham in the first half but we also saw a good Brighton team in the first half. They made it difficult for us but the resilience of the players kept us going and a few changes helped us.
Brighton manager Graham Potter, talking to Match of the Day: "We didn't make the advantage count enough. We started the game well and forced a tactical change because we dominated, but the red card changes the game and we've got to make sure we don't get caught.
Brighton boss Graham Potter, speaking about goalkeeper Robert Sanchez after he made a number of excellent saves: "I made the decision to go with Rob, he has some incredible attributes we wanted to use.
Leicester manager Brendan Rodgers to BBC Sport on James Maddison: "He has such quality. What makes it even better is he hardly trained at all this week. He had an issue with his knee so we took him out of our midweek game.
Liverpool captain Jordan Henderson to Match of the Day: "The first half there were one or two things we could improve on. We maybe should have scored the second. Overall we have to be happy with the performance.
Brighton manager Graham Potter says he is 'delighted' Danny Welbeck scored his first goal"Our second was a really good team goal and a great finish by Solly March," said Brighton manager Graham Potter.
Tottenham boss Jose Mourinho, speaking to BBC Match of the Day: "It wasn't a surprise because I knew Brighton were a very good team with a very good coach. They created lots of difficulties but we had a very good reaction after they equalised.
Brighton boss Graham Potter, speaking to BBC Sport: "Frustrated, certainly the second half.
"Credit to West Brom, I think they responded well. They played better in the second half and pushed us back and they deserved their equaliser.