Derby head coach Paul Warne blamed the “fear” factor for his team’s failure to defend the lead against Shrewsbury.
Max Bird fired Derby ahead only for Aaron Pierre to equalise three minutes from the end of normal time.
It was a disappointing end to what had been a frustrating afternoon for Derby, with Shrewsbury doing a good job of restricting them to few clear chances.
Warne said: “I thought first half was my fault, I picked the wrong shape for the game. We didn’t really get out and we looked a bit edgy.
“I changed the system and we looked a lot more like it second half and created some decent opportunities.
“We got the lead and then it’s all about getting the second goal, but we didn’t play with enough personality to create enough chances to get a second.
“My regret is we didn’t play with enough personality and freedom when we were leading and it looked like we played with a little bit of fear and you’re never going to get success off that.
“I’m hugely disappointed that we worked all week to get the win and we’ve lost it on a throw-in. It does feel like it’s two points lost (especially) when it’s that late on.”
Derby made the most of one of their rare openings in the 54th minute with Bird firing a low shot under Marko Marosi following a corner.
Marosi turned behind a Conor Hourihane free-kick before Shrewsbury stunned Pride Park when Mal Benning got behind Derby on the left and found Pierre, who beat Joe Wildsmith with a low drive.
Wildsmith saved from Carl Winchester but Derby almost won it in stoppage time as Curtis Nelson headed against the bar and Tom Barkhuizen was denied by Marosi.
Shrewsbury head coach Paul Hurst said: “I’m pleased with a point, I think we’d have taken that before the game, although we came here not just to take a point or hang on.
“The feel I had was I don’t think they caused us too many problems but when we fell behind you’re concerned about how the rest of the game would pan out, but it seemed to spark us into wanting to play more.
“That’s a frustration but pleasing as well – as in, was that a great response from us or from them taking a backward step because they got themselves in front?
“We started to pass the ball more and had a spell where we were good. I still think there’s got to be more belief from the players at times, although overall I think we deserved that point.”