Maupay was a close-season target of Blades boss Chris Wilder, before he elected to join Brighton.
United splashed £20m on Oli McBurnie but it was Enda Stevens who put them ahead against Brighton, only for Maupay to equalise shortly after.
The draw left United seventh in the table at the close of the weekend, with 11 games to go. They enjoy a blank weekend this Saturday because their planned game, away at Aston Villa, has been postponed owing to Villa's participation in the Carabao Cup final at Wembley.
And Maupay, the former Brighton striker, said: “Against teams like Sheffield United, you have to defend with 11 players to get anything and that is exactly what we did starting with Glenn [Murray] and myself right through the team.
“Our quality in possession was not that good. They were better than us in that area so we had to rethink. The difference was that we realised we had to change our ambitions.
“Sometimes in football, you cannot always play the way you want. You have to play to suit the game.
“We are in a relegation battle. But in this league, every team has problems against Sheffield United. Not too many have coped like we did today. We showed great battling qualities and that is what we will need for the rest of the season.”