Carrick signed a two-year deal to extend his stay at Old Trafford on Friday, before guiding United to a 3-0 victory over Brighton on the final day.
It brings to a close a positive season for United, who secured Champions League football and a third-place finish.
Carrick's arrival in January also resulted in a run of 12 wins in 17 matches, including victories over Arsenal, Manchester City, Liverpool and Chelsea.
Asked about a future under Carrick in the long term, Fernandes told Sky Sports:
"It's a very important step for our club. We need stability in terms of managing.
"And since Michael came to the club, I've known how he works; I worked with him already, but you know how calm he is. He gives calmness to the team.
"But also the moments he needs to put some pressure on us. He does it too.
"He knows the club. He knows what it means and what it demands to be at this club.
"We are very excited for what's coming, as we always are but as you said, we finished strong and that's a good sign for what's coming."
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