Edozie was hoping to go out on loan for the season to Glasgow Rangers in Scotland.
However, he was not able to secure the move, with the 21-year-old set to stay at St. Mary’s until the winter at the least.
Martin told the Daily Echo: "What frustrated me was how late it fell through and it wasn't on our end.
"I think it's a bit unfair to Sam really. It's a bit disappointing but it is what it is. Every club has their prerogative and their priorities in the transfer window.
"I was gutted for Sam because it was too late to then find another opportunity to go and play football.
"He'll get to work like everyone else now. Get his head down, work really hard and try and get himself into the squad and into the team.
"He wasn't in it today because of the speculation but also because Sam Amo deserves to be in the squad more than he does right now.
"That's my opinion and that won't be everyone's opinion. It definitely won't be Sam Edozie's. But unfortunately, I'm the guy who takes that hope or the opportunity of him playing away.
"It's the hardest bit of the job. So we'll have a chat. We had a couple of messages already and we'll have a chat on Monday.
"He'll be fine. He needs to find a way to get himself back into the group and really impact things."