However, Martinez is more positive regarding the injury following a scan and is hopeful of having the former Manchester United man back available to him before the end of the season.
"It was a real disappointment on Tuesday night. I was watching the game and straight away you could see it was an innocuous incident and that is normally when you pick up really bad injuries. I was really fearful of expecting the worst but with the scans on Wednesday we are very positive now," Martinez told PA.
"It is an ACL but the whole structure of the knee is perfectly fine and it is going to be straightforward surgery. I'm looking forward to seeing him back hopefully this season and that in a way was good, positive news taking into consideration what it could have been.
"The ACL is ruptured but his knee reacted really well and nothing else was damaged - in those sort of actions you normally get more than one structure damaged and some of those are very difficult to repair.
"You can imagine it is really disappointing to lose Darron for whatever space of time but we are all very positive that when he comes back he will come back stronger. We will use this period to get Darron working on other aspects of his fitness and making sure his knee is going to be perfectly repaired and ready for whenever he is back."
Gibson has only managed 96 minutes of action for Everton this season having picked up another knee injury at the start of the current campaign.