"We're delighted for Fabio because he has been a great servant. His brother [Rafael] is doing a great job for us here as well. We wish him well. He had one or two options but, in the end, we felt we couldn't get him enough games," Moyes told MUTV.
"I said to the players, if you feel I'm not getting you enough games, come and see me. Fabio felt that so he's got a move to Cardiff. With Wilfried Zaha, I'd said to him during the summer that we wanted to get him games. If he played, then great, but if he couldn't, we'd get him out on loan.
"We had one or two offers for him but just felt Cardiff, at this moment in time, might be the right club. With Ole going there as well, he knows how the club works here and exactly what we do with the players so hopefully it will be a good move for Wilf."
Neither Fabio nor Zaha will be eligible to play for Cardiff against United in tomorrow's Premier League fixture between the two sides.