Derby manager Wayne Rooney pointed the finger at goalkeeper Ryan Allsop after his late mistake allowed Luton to secure a 2-2 draw.
Derby led twice at a rain-swept Pride Park only for Luton to peg them back, although both sides will question the goals conceded.
Luton skipper Sonny Bradley lost the ball to Jason Knight who set up Tom Lawrence to fire low past Simon Sluga in the 20th minute
The visitors made a double substitution after 30 minutes and one of those levelled in the 48th minute when a long throw was flicked on at the near post and Fred Onyedinma dived to force the ball home.
Knight restored Derby’s lead with a low drive that went through Sluga on the hour only for an Allsop error to see Luton equalise seven minutes from time.
He came for a cross but failed to get there and Elijah Adebayo headed into the unguarded net.
Allsop was beaten again when Onyedinma lobbed him from a tight angle but the ball came back off the bar.
Rooney said: “It was a tough one to take. I felt we did enough to win the game, scored two good goals and then we conceded two very sloppy goals which we haven’t been doing.
“We know long throw-ins are difficult to deal with but we’ve dealt really well with them of late so that was disappointing to concede from that.
“We had a great reaction with a very good goal from Jason Knight but then obviously it’s a clear mistake from Ryan Allsop which has cost us three points.
“We are competing in every game and we know we are a hard team to play against but I’m frustrated tonight with one point.”
Luton manager Nathan Jones said: “The performance levels were nowhere near and we looked energy-less for lots of the first half.
“We shot ourselves in the foot, we made changes and we started the second half like a house on fire, got the goal but then a bit of a sucker punch again.
“We had to show a load of character and I’m really pleased after two away games and four points against two really difficult sides.
“Considering we were way off our levels we’ve come away from a difficult place with a point which shows we have something about us.
“Apart from two 45 minutes we’ve been outstanding this season and deserved more and we’ve gone to some difficult places.
“We should be higher but I think the reason we’re not is we probably haven’t taken chances when we’ve been on top.”
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