The ex- Manchester United midfielder subsequently picked up a thigh injury against West Brom and hasn't played for Everton since then, though the club is hopeful he will make the trip to Reading tomorrow week.
According to Coleman, Gibson has been a huge addition to Everton and he believes that his club-mate will also make his mark at international level.
"He has been unbelievable since coming to the club. Him and (Nikica) Jelavic, the whole form of the team really improved and the sooner we get him back the better," said Coleman.
"He will be a massive player for Ireland. I was in a couple of Ireland squads with him when he was at Man United, but I didn't get to really see how good he is until he came to Everton. His range of passing is superb -- ask any Everton fan about him and they will sing his praises."
But as for Gibson's falling-out with Trapattoni, Coleman -- who was also denied game time at the Euros -- says that he doesn't know if the two have cleared the air yet.
"Everyone knows that Darron pulled himself out of one of the squads but I haven't really spoken to him about it," he said.
"We see each other every day at training but it's his thing and it's not up to me to tell him to come back. It's his own decision."
Ahead of Wednesday's friendly with Greece, Coleman is more concerned about strengthening his own claims for the right full-back position where he has been shining for Everton this season.
Despite his excellent club form, the former Sligo Rovers defender has only played two competitive internationals -- against Germany and the Faroe Islands -- and is determined to prove himself to Trapattoni.
"I'm not bitter about not getting picked for the Euros, absolutely not. I was in and out of the team last year, but it's definitely my ambition to get to a major tournament with Ireland," he said.
"I've got my chance now and obviously I would have liked more in the last few years, but there are a lot of good players in my position. But I never gave up hope and I got in. It's up to me to try and stay in the team for as long as I can.
"If selected against Greece next week, I need to do well and try impress the manager and Marco (Tardelli)."