Everton were handed a huge blow earlier on in the season after Leighton Baines was ruled out with a long term injury but young Galloway has managed to step up to the plate in brilliant fashion and has been a revelation at left-back so far this campaign.
Martinez has revealed that Galloway has impressed everyone with his maturity and has backed the youngster to become a 'special' player in the future.
The Spaniard said: "Brendan keeps surprising everyone. His maturity is very impressive. He takes each game as it comes. I haven't seen him needing rest or to be taken out of the team.
"You need to measure it week to week and let football make the decision. I don't think there's a general rule for someone who is 19 and how many games you need to give them. It doesn't work like that.
"We've been pleased how he adapted to different demands and he's someone who is going to be quite special for the future."