Phil Foden was sent off after 23 minutes at Old Trafford following an altercation with Bruno Fernandes, forcing City to change their approach for the remainder of the match.
However, Erling Haaland struck on the hour to give City a crucial lead, and they held on for victory in the 199th derby between the two sides.
Maresca admitted the dismissal changed his team's plans but felt United also found it harder to play against a City side that had dropped deeper.
"We had a plan 11 v 11 that after the red card completely changed," Maresca said.
"The game with 10 men became more difficult for us but also for them. They are a team that loves to play in transition and they love space in behind.
"But with 10 players we just dropped, waiting for them, and we didn't concede any transitions or space behind. That's why I say it became more difficult for us and for them."
Maresca used half-time to convince his players that the match was still there to be won.
His message had the desired effect as City remained disciplined before Haaland's decisive goal.
"The message at half-time I said to the players was the game was more difficult for us – but also more difficult for them," he said.
"So keep believing we can win the game. Believe, stay in the game and we can win this game.
"To win with 10 men is already special, but it was even more special when it's a Manchester derby for the fans, for the players and the coaching staff."
Maresca also gave his view on the two major VAR incidents, starting with Foden's red card and then Haaland's goal, which was checked before being awarded.
"I think the red card for Phil Foden is a red card. But I also think in the same action it's a red card for Bruno," he said.
On Haaland's goal, Maresca added: "The fourth official told me that Erling was onside and they were just checking the entire action. Nothing more to add on the goal."
City were forced to defend their lead late in the match and needed a big save from Gianluigi Donnarumma to deny Bryan Mbuemo as United pushed for an equaliser.
Maresca praised the goalkeeper for producing when his team needed him most.
"Big players score at vital moments. Big keepers make big saves at vital moments like Giorgio at the end. It was a great save," he said.
City will now turn their attention to the EFL Cup, with Norwich City visiting the Etihad Stadium on Thursday in the third round.
