Both sides recorded away wins on Friday, leaving them second and third respectively in the Championship table with three games left to play.
Speaking after overseeing the Rams' victory at the Keepmoat Stadium, McClaren told reporters: "It's too little, too late [for us].
"They are going to go up. I can't see them falling over now. Getting over the line is hard, but I can't see it."
On his side's display, he added: "It's about performance and we were bitterly disappointed with the first-half performance.
"The second half was better but we can't play like that in the first half, better teams will kill us. We have to do better."
Derby can finish no lower than fifth this season, meaning that an appearance in the playoffs is guaranteed should they fail to overhaul Burnley.