Despite taking the lead through a Steven Gerrard penalty awarded after just 32 seconds two Jon Walters goals, either side of a Kenwyne Jones header, extended Liverpool's winless streak at the Britannia Stadium to five matches.
Rodgers felt his side needed more resilience to combat Stoke's physical pressure. "We conceded soft goals after a great start," he said. "A bit of magic by Luis (Suarez) got our first penalty of the season, Steven sticks it away perfectly and we are 1-0 up at a difficult place to score goals."
He added: "We wanted to gain the initiative from that but the nature of the goals we conceded was very soft and if you do that it is always going to be uphill in terms of getting a result.
"The first one is unfortunate as Martin Skrtel slips and Walters finished well but the other two goals we have to be better than that. It was too soft: a corner that sneaks in at the near post and then from a throw-in.
"You have to be better in those moments, especially against Stoke because you know that is a big part of their strength. It is not all about football. You have to earn the right to play, particularly coming here. I have no doubt about the characters we have but tonight it was too easy."
Stoke boss Tony Pulis was pleased with the way his side fought back after conceding the early goal, saying: "It was a great result and performance. I thought the response after going a goal behind after just 30 seconds was absolutely fantastic and epitomises what the group are about at the moment.
"We've played games where we've created more chances and finished 0-0 so we have been creating the chances but not been taking them. We have tremendous respect for Liverpool and we are very proud to host a game against such a great club and when you beat them it gives you great delight, it is always special."
Walters second, controlling a flick-on from Jones on his chest and volleying past Jose Reina, was the pick of the goals and took him level with Ricardo Gardner as the club's all-time leading Premier League scorer with 18.
"It was a great finish and I am very pleased for Walts," Pulis added. "His commitment to the group is fabulous and he is a good player as well."