The Manchester United captain spoke after helping his side recover from two goals down to beat Roma 3-2 in the Champions League, scoring a penalty that sparked the comeback at Old Trafford.
Fernandes had been left out of the starting line-up for one match after publicly criticising Carrick's tactics following the 4-1 defeat by Como. He returned to the team for the subsequent Premier League loss to Chelsea and was again selected against Roma.
The midfielder dismissed reports that the decision to leave him out had caused a breakdown in his relationship with the manager.
“There's been a lot of speculation in the media, a lot of lies around between me and the manager that we had to clear the air,” Fernandes told Prime Video.
“None of that happened, the manager took a decision to put me on the bench because I wasn't performing and that's fair. Everyone thought it was a punishment for the words that I had and if it was he was right, the manager is the one who makes the decision.”
Fernandes was also emphatic that the episode had not affected his confidence in Carrick or his determination to win with United.
“It doesn't change the belief I have in the manager and the staff and every player in this club and it doesn't change my aim to win every f***ing game,” he said.
The Portugal international's penalty arrived in the 58th minute, after his first attempt was saved but ordered to be retaken because of encroachment. It gave United a foothold after Matías Soulé and Donyell Malen had put Roma 2-0 ahead.
Fernandes then provided the assist for Matheus Cunha's equaliser in the 83rd minute. Cunha struck again three minutes later to complete the turnaround, although he was sent off in stoppage time.
Fernandes acknowledged the frustration felt by supporters during United's difficult run, which had extended to nine matches without a victory before the Roma game.
“It's been a long time, we didn't get a win, it's been frustrating for them as much as us too,” he said.
“Fans want to win games. They are used to seeing this club at the top, winning trophies and it's been frustrating to see the club in this situation.”
He hoped the result could provide a starting point for improvement, adding: “Today was important to get a win. We knew after that we still had the fans with us, we felt we could change it with a goal and something and fortunately we did it today.”
United host Aston Villa on Sunday before the international break.