Rooney, who appeared alongside Carrick for both Manchester United and England, was dismissed this week after just 15 games in charge of the Championship club.
Rooney won a huge haul of trophies at Old Trafford, including five Premier League titles and the Champions League.
He also established himself as record goalscorer for United and England before Harry Kane bettered his international record.
But Carrick, who also boasts an impressive number of medals, knows that counts for little once in the dugout, with contemporaries Frank Lampard and Steven Gerrard also having endured difficult starts to their coaching careers.
"It's not easy, it's challenging," he said on Thursday. "Player or no player, it almost becomes irrelevant in some way.
"You are judged for how good or how successful you are or what you're achieving in the role that you're in.
"It's me sitting here now, the boys are playing on Saturday, I'm in a totally different role. It in some ways becomes irrelevant what's gone on in the past, it's about what's next."
Carrick, whose Championship side host Aston Villa in the FA Cup third round on Saturday, is convinced Rooney has too much talent not to emerge from his disappointment at St Andrew's and succeed as a boss.
In his first managerial role, Rooney was unable to stop Derby being relegated from the Championship in 2021 after they were hit with a points deduction for financial issues.
He also had a spell in charge of American side DC United, joining in July 2022 and leaving after failing to qualify for the MLS play-offs in October this year.
"I'm bitterly disappointed for Wayne, knowing him as a friend, and I know he'll bounce back, I know he'll be a success," he said.
"He's too good, he's too knowledgable and he's had too much experience to not use that in the right way."
