Former Ibrox boss McCoist stated this week that Rangers were quietly building their way to restoring former glories and fans should not expect a title challenge this season.
McCoist claimed Celtic were “comfortably” the best team in Scottish football ahead of Saturday’s derby at Parkhead.
But Warburton, who led Rangers into the top flight and the William Hill Scottish Cup final in his first season in charge, does not feel he and assistant David Weir have the luxury of time.
“I’m not going to be given three years to get the club back to the top flight of Scottish football,” he said. “It doesn’t work that way.
“The expectation of the club, let’s be realistic, if I turn round and say I’ve got three years to get it right? I don’t think so.
“So we have to be quicker than that. If those timescales are accurate, and I hope they’re not, then I won’t be here. David and I know that.”
Warburton added: “The game’s about opinions. Ally is a very experienced man, huge Rangers connections, quite rightly legendary status at the club.
“So Ally is entitled to his opinion and I’ve seen Walter (Smith) speaking and various other people. The beauty of the game of football is everyone has got a different opinion.
“It’s great Ally voices his own personal opinion. Mine might differ slightly but that’s the game we love.”
Meanwhile, Warburton revealed that defenders Lee Wallace and Danny Wilson were in line to play at Celtic Park.
Wallace pulled out of the Scotland squad last week with a muscle injury while Wilson missed the draw at Kilmarnock with a calf strain.
Warburton said: “Lee Wallace is fit. Danny, we hope, is very, very close and he’s looking good this morning, so fingers crossed. But Lee Wallace is definitely fine.”
Martyn Waghorn and Josh Windass are both fully fit following hamstring injuries while Jason Holt could feature off the bench after an ankle problem. Joe Dodoo and Matt Crooks are definitely out.