Ferguson announced earlier this month that he is retiring after over 26 years in charge and the game at The Hawthorns was his 1,500th as United manager.
He watched the Premier League champions let a 5-2 lead slip as West Brom scored three times in the final 10 minutes as Romelu Lukaku's hat-trick helped to secure a point.
It was a first 5-5 draw in Premier League history and the entertainment on offer was perhaps a fitting send-off Ferguson.
The Scot will be replaced at Old Trafford by David Moyes and Carrick offered his thanks to Ferguson before focusing on a fresh challenge.
"I want to thank him for everything he's done, he's done much more than us," Carrick told Sky Sports.
"It was a funny time in the dressing room because of the situation.
"It is starting to sink in and we've had a couple of weeks to digest the news.
"We're ready to move on. We've had a busy couple of weeks and there is a new challenge ahead for all of us to look forward to."