Michael Mifsud wasted a great chance when Jon Macken sent him clear in the 21st minute and he was almost in again when a back-pass from Andy Todd fell short in the 47th minute.
Derby offered little and the visitors were unlucky when a cross from substitute Mounir el Haimour came back off the inside of a post in the 71st minute.
The best opening fell to former Derby striker Macken in the 78th minute when a chip from Hugo Colace set him up eight yards out but goalkeeper Stephen Bywater turned his volley over the bar.
Davey, whose side are hovering above the bottom three, said: "Ordinarily a point at Derby County would be something for a big celebration, but on this occasion, it has to go down as a disappointment.
"That's up there with our best performances of the season. We dominated the first 45 minutes and we were better than them in the second half.
"Jon Macken had a great chance but their goalkeeper pulled off an unbelievable save, you won't see better than that all season.
"We also hit a post, although that was probably not intended, and Michael Mifsud had a couple of chances when he was through on the goalkeeper, and that's why I think it should have been a three-point game for us.
"It's very frustrating to create so many chances and only end up with one point, but when you are down where we are, you don't get lucky breaks."
Barnsley could have paid for their misses two minutes from the end when Gary Teale got away down the left, but his cross was just too high for Mile Sterjovski who headed over.
Derby manager Nigel Clough accepted his team had been off the pace and had goalkeeper Bywater to thank for denying Barnsley victory.
Clough said: "We are relieved that we've come away with a point when we were under par.
"We're very pleased with a point, but not pleased with the performance, although you have to give Barnsley a lot of credit.
"They played exceptionally well today and we didn't, but we've got a point out of it and we are better off than we were before the start.
"We didn't want to build the game up too much and say it was a must-win match, but it was a more tentative performance than the recent ones at home have been.
"The goalkeeper was brilliant. He kept us in it with a couple of one-on-one situations and then the save from Macken and who knows how important that point is going to be at the end of the season."