Scotland international Conway was one of the unlucky players to miss out after Mackay was forced to trim his squad to the required 25-man limit.
Conway, who handed in a transfer request last season after growing frustrated with his lack of first-team action, is now set to be allowed to go out on loan with Mackay conceding he was unlikely to be playing much in the Cardiff side this season.
"It was difficult to pick the squad and trim things down, but we did that as Premier League rules state we must," said Mackay.
"It was unfortunate for Craig, but he has always said that he desperately wants to be playing football.
"When he came to me about the transfer request last season that was very much what our conversation was about.
"That is fine and I totally understand that, but obviously I could not give him any assurances about that at this club.
"With the signing of Peter Odemwingie, Craig's chances were inevitably going to be limited.
"This was not a cold hard decision. Me and my staff sat down and chatted. We looked right across the squad and tried to come up with the correct balance and we believe we have done that.
"But also I believe it is for the best for Craig too. He is player who is really establishing himself with Scotland at international level under Gordon.
"To do that he will need to be playing games and that was going to prove difficult here."