United was 3-0 up after 30 minutes but a sensational hat trick from Romelu Lukaku helped the Baggies get back into it late in the game.
Shinji Kagawa, Alexander Buttner and an own goal from Jonas Olsson had put daylight between the two sides and at one point United was 5-2 up, but it was not to be the perfect end to Ferguson's 1,500th game as boss.
However, Carrick believes that the Scotsman can walk away from the touchline fulfilled, telling reporters: "Ferguson can retire satisfied. It has started sinking in now and there is a new challenge ahead for us now."
The 31-year-old also insists that the changes through which the club will go over the summer will not be particularly drastic and that the team is experienced enough to stay at the top.
"I don't think the changes will be too difficult for us," he added. "As a squad we're experienced. I'm sure the same teams will be at the top.
"We've thanked Sir Alex for everything he's done and he's thanked us. We're ready to move on."
One of United's goalscorers at the Hawthornes, Javier "Chicharito" Hernandez, was left irritated with the draw and admits that the team was craving a perfect sendoff for the retiring manager, as well as Paul Scholes, who was also bowing out of professional football.
The Mexican striker told the press: "We are frustrated. We wanted to win this game for the boss and Scholesy. Gaffer said he will remember this game."