United were beaten 1-0 at Old Trafford on September 13, despite City being reduced to 10 men early on following Phil Foden's red card. The result left Carrick's side with four points from their opening four Premier League fixtures.
Their league campaign began with a 2-0 loss away to Hull City before United claimed their first victory by defeating Ipswich Town 5-2 at Old Trafford. They subsequently drew 2-2 with Everton at Hill Dickinson Stadium.
Carrick will now want his players to put the derby disappointment behind them as they turn their attention to Brighton in the EFL Cup third round tonight.
United have already enjoyed success in Europe this season, opening their Champions League campaign with a commanding 4-0 home victory over Sabah FK on September 10.
"Sunday's Manchester derby was extremely frustrating for a number of reasons," Carrick told the club's official website, "but now we have to move on quickly and get back to winning ways.
"The fixtures are coming thick and fast ahead of the international break next week; we have a squad full of talent with everybody pushing to play.
"As a group of coaches, players and staff, we want to play as many games as we possibly can this season, so we need to progress through matches like this one and make sure we keep competing on every front."
