Louis van Gaal launched a 20 million euro bid for the Argentina defender earlier this week, but saw the approach rejected by the Portuguese outfit.
That prompted Rojo to reportedly miss training on Wednesday in a bid to force the move, but 24-year-old has now apologized for his actions and admitted to acting rashly following the failed bid.
"It was all a misunderstanding, I was a hothead. I'm sorry for what happened because I feel that I was unprofessional," he told the club's official TV station. "Now I will try to correct the situation.MORE: Coach Ted Lasso returns! | Porter challenges Guardiola | WAGs
"Yes, obviously [I trust the club]. The club trusted me when my career wasn't at its best. They gave me an opportunity to play for a top team in Europe. So I thank Sporting and the people who work here.
"But I want to stress that I'm very happy at the club, and I like the way I'm treated and the care they give me."
Rojo and Sporting’s president Bruno de Carvalho reportedly nearly came to blows during a meeting earlier this week, a claim the defender vehemently denies.