Midfielder Monti, 20, had become a regular fixture at left-back towards the end of the season after impressing there when asked to fill in for the injured Kevin McKinlay.
And although Moore was keen to retain the former Celtic youth's services, he has now conceded the player is unlikely to be back at Cappielow after two contract proposals were rejected by his agent.
He said: "We offered Carlo a deal here for next season, but that looks to be dead in the water now.
"We made two offers and those were both knocked back by his agent, who said they were less than he was willing to accept.
"After that, we decided we would be withdrawing our offer. As far as we're concerned, there is no longer a deal on the table and that's where things are at.
"So, at the moment, it looks like he won't be coming back here next season as we won't be going back with an improved offer. That's the bottom line."
The departure brings to an end a three-year spell with the club in which Monti made 61 appearances and scored nine goals, including one from the penalty spot in the final match of season against Stirling Albion.
However, one player Moore is still hopeful of retaining is Frenchman Fouad Bachirou, who is yet to make a final decision on the offer made to him earlier this month.
Moore added: "We've also offered Fred a new contract, but we're still waiting to hear back from him.
"The situation with Fred was a wee bit more complicated as we had to send the contract to his agent in France.
"So we're still trying to get something sorted there, but I'm hopeful he'll be back next season."