Giovanni van Bronckhorst’s side capped a memorable week by knocking out Braga to earn a spot in the Europa League semi-finals before overcoming the Hoops just four days later to set up a Scottish Cup final meeting against Hearts.
The back-to-back victories were made all the more impressive given the Ibrox club were taken to extra-time in both games.
That will have given the Gers squad added belief that they can make inroads into their six-point league deficit with just five matches remaining.
Rangers and Celtic will go head to head for a fifth and final time this season at Parkhead next Sunday.
McCoist recognises it will take something special for the Scottish champions to retain their top-flight crown as he claimed it would be ‘the biggest collapse of all time’ from Celtic if they were to throw away their advantage.
Asked by Laura Woods on the talkSPORT breakfast show if the two huge wins in just four days will boost their title challenge, he said: “I hope so. You’ve got to keep going. You’ve got to believe and keep going.
“It would be one of the biggest collapses of all time however, you’ve got to believe it can happen.
“It’s been a great week. I was working at the game (on Thursday) and it was brilliant. The atmosphere was amazing.
“They should have been home and dry, honestly it could have been 5-0 then we lost a goal right in the last seven minutes to take it into extra-time, but that’s just what we do.”
Meanwhile, ex-Celtic striker Charlie Nicholas has labelled Rangers’ wild post-match celebrations after Sunday’s Old Firm derby semi-final win “extreme”.
Scott Arfield’s strike and Carl Starfelt’s late own goal saw the Gers come from behind to edge out their bitter rivals in a thrilling encounter at the national stadium.
Writing in his Daily Express column, Nicholas said: “Rangers’ celebrations at the end of their Scottish Cup semi-final win over Celtic were a bit extreme.
“They deserved to go through because they were the better team at Hampden but there is still a lot of work to be done before they can really celebrate.
“I am not being bitter towards Rangers because I know the intensity of the emotions after an Old Firm derby.”