The Reds went a goal up in the early stages of the match through a Steven Gerrard penalty after Luis Suarez was brought down in the box by Ryan Shawcross. But the Potters soon equalised, and went on to take a two-goal lead, thanks to a Jonathan Walters double and a fine header from Kenwyne Jones.
And Rodgers has expressed his disappointment at the nature of the goals his team conceded, explaining that his side must defend better if it is to take points away from such matches.
“It was a great start for us, getting our first penalty, but we just gave away poor goals tonight,” he told Sky Sports. "I think all three goals were actually quite straightforward to defend. A direct ball, and obviously Martin Skrtel slips, which was unfortunate.
“The other two goals, we've got to be much better than that. That was a disappointment really. We got into some good areas but ultimately, when you come to places like this, it's a difficult place to come and you've got to defend better or else you'll get nothing.
“We deserved nothing because of that.”
However, the former Swansea manager also moved to praise Tony Pulis and his Stoke side, which is now unbeaten in its last nine matches.
“They [Stoke] probably don't quite get the credit they deserve and Tony's done a brilliant job here in keeping them in this division and progressing,” he added. “They've got some terrific players and they do what they do very well. But from our perspective it was poor defending.”