The Ibrox men harboured hopes of winning all their matches in the third-tier this season but were undone with a stoppage-time equaliser from Jamie Longworth.
McCoist admitted his team were below par, and felt the visitors could have got more from the game.
He said: "I will be 100 per cent honest with you - I actually couldn't give a monkey's about the record. I really couldn't.
"I'm not interested in the record, I'm only concerned about the level of performance that we gave and it was extremely disappointing.
"It was a really disappointing day for us. Certainly I'm of the opinion that Stranraer more than deserved their point."
Stranraer boss Stephen Aitken reckoned his side could have taken all three points had it not been for what he described as a "dodgy" penalty decision by referee Andrew Dallas, which led to Rangers taking the lead through Lee McCulloch.
"I'm delighted, over the moon. To come here and perform the way we did was pleasing," Aitken said. "I thought we thoroughly deserved the point. For long spells we were in control of the game.
"If it wasn't for a wee dodgy penalty decision we might have got more.
"But if somebody had said they would have given me a point for a Christmas present, I would have bitten their hand off."