Former Brisbane Roar midfielder McKay has featured just once for Ally McCoist's men since he completed a move to Scotland in August.
McKay said: "I've played a few reserve games but it's not the same as playing first-team football.
"It's a massive club and I want to start playing.
"I played in the first game as soon as I got there but haven't been involved the last couple weeks.
"I'm a bit disappointed but I've got to get my head down.
"We've got a massive squad at Ibrox and the boys are winning games so I'll just have to keep working hard. When my chance comes I'll need to make sure I'm ready to take it and hopefully keep myself in the team."