The defender has struggled with injuries since moving to Selhurst Park, but was back in the side on Saturday and scored his first league goal in eight years in the 2-2 draw with Leicester.
Despite their poor recent form, Palace remain in the play-off places and Gabbidon wants to help them get over the line.
"As a footballer you always want to play," he said.
"It's been a stop-start kind of season for me. I joined late and the team was doing really well and I couldn't really get in the team which was understandable, and when I did play a few games I ended up getting injured which was disappointing.
"It's been a bit of an up and down season but the lads have been fantastic. I'd like to stay in the team if I can."