The Reds took an early lead through Steven Gerrard’s second-minute penalty but conceded twice in seven minutes as Jon Walters and Kenwyne Jones hit back for the Potters by the 12th minute.
Rodgers felt that the three goals Liverpool gave up – with Walters adding a third early in the second half – could have been avoidable as his side slipped to 10th on the table.
"It was a great start for us, getting our first penalty. Coming away from home and starting like that was great, but we gave away poor goals. All three of them were actually quite straightforward to defend,” Rodgers told Sky Sports.
"The first one, Martin Skrtel slipped and was unfortunate but there were two goals where we have to do much better with and that was the disappointment really.
"We got into some good areas but when you come to places like here, you've got to defend better or else you get nothing and we deserved nothing because of that.
"Everyone knows the strengths of Stoke and they do it very well, but when you've prepared to deal with it's even more disappointing. It was a corner, a throw-in and a direct ball.
"Stoke don't quite get the credit they deserve. Tony Pulis has done a brilliant job here to keep them progressing. They do it very well. But from our perspective, it was poor defending."