Ex-skipper Greacen, 28, who had been at Cappielow for seven years, has moved on after only featuring in four matches this season.
But as one player departs, another two look set to stay, with Grant Evans and Sean Fitzharris both agreeing to extend their loan deals until the end of the season.
Moore says he understands Greacen's frustration, but admitted he could not see the big defender making a return to the first team.
He told the Tele: "I've brought in Marc Smyth and Stuart McCaffrey, who I feel have done a great job, so I just thought Stewart could do with a fresh start.
"I couldn't see him getting back in the team if I'm honest. I want players that can get the ball down and pass it out from the back.
"Stewart had indicated to me that he wanted to play and I couldn't guarantee him that. He's at an age where he needs to be playing every week.
"He came in for a couple of games against Queen of the South and Cowdenbeath and did reasonably well.
"But I spoke to him and said, if it came down to it, my two centre-halves would be McCaffrey and Smyth, and that he would only get in if there was an injury to one of them.
"He just wanted to play football and I spoke to the chairman, who wasn't too averse to letting him go.
"With no disrespect to Stewart, he was finding it difficult to get into the team and, although the table doesn't maybe show it, we haven't been losing a lot of goals.
"But he's been a great servant to the club and I wish him all the best wherever else he goes."
But while Greacen has gone, yesterday saw Grant Evans and Sean Fitzharris both verbally agree new deals until the end of the season.
Defender Evans has been on loan from Hamilton since the summer, while Celtic startlet Fitzharris had impressed during a short loan stint earlier in the campaign.
Moore said: "I spoke to Billy Reid at Hamilton and he said he's happy to give us Grant on a six-month loan deal until the end of the season.
"And I spoke to John Park at Celtic and he said he is happy for Sean to stay on as well.
"The two of them are happy to come back and fight for a place in the team. They're both young players and that's something we want here.
"I've spoken to both of them and said if they don't get offered anything at their clubs next year there is a chance they might be offered deals here.
"They're both happy to come and we're hoping to get the deals tied up by the end of the month."
Meanwhile, striker Jonathan Toto has also left the club.
Moore said: "He's in France just now and we've told him we won't be taking him back in January."