Following United's 2-0 midweek UEFA Champions League loss away at Atletico Madrid, Martinez boldly criticised the club's transfer policy this summer, for which the Argentinian has since apologised and been punished by the club.
Carrick declined to offer an update on the internal punishment handed out - which is likely to be a fine - but the former midfielder confirmed Martinez is available for the weekend Premier League trip to Leeds United.
"It's done really. We've moved on from that. It was one of those things. He's come out and acknowledged the situation and as a group we've moved on.
"It's not a drama for us as a group. The boys have trained really well, there's a really good feeling around training this morning.
"From the outside, you are after some big information about big discussions, but it's pretty simple. We all understood the situation and what it meant. He made his statement and acknowledges it was a mistake and that's it really."