He said: "It was a great start for us, when you come away from home it's great to go a goal up, but we just gave away poor goals tonight [Thursday]. I think all three goals were actually quite straightforward to defend.
"Obviously Martin Skrtel slips (for the first), which is unfortunate, but the other two goals we've got to do much better than that. So that was the disappointment really.
"We got into some good areas but ultimately when you come to places like here, which is a difficult place to come, you've got to defend better or else you get nothing, and we probably deserve nothing because of that."
Rodgers also praised Stoke and the work being done by Pulis.
"I've always said they probably don't quite get the credit they deserve. Tony's done a brilliant job here, keeping them in this division and keeping them progressing," he added.
Prior to the victory over the Cottagers, Rodgers' side had suffered a surprise loss at home to Aston Villa and the Northern Irishman accepted the up and down nature of their results was hindering their attempts to move up the Barclays Premier League table.
"Consistency is the biggest thing for the group," he said.
"We were terrific at the weekend but you have to be able to put some runs of games together - if not you will make two or three steps forward and then take one or two back.
"Maybe that has been the nature of the group over the last couple of years.
"We are looking to improve that and there is an awful lot of work to do."
Two-goal hero Jonathan Walters hailed his side's character and work ethic after Stoke recovered from a nightmare start to claim a 3-1 Barclays Premier League win over Liverpool on Thursday.
There were only 32 seconds on the clock when Luis Suarez won a penalty which Steven Gerrard converted to put Liverpool ahead at the Britannia Stadium.
However, Stoke stormed back and within 10 minutes had turned the game on its head through goals from Walters and Kenwyne Jones, and then a second from boyhood Everton fan Walters just after half-time sealed the victory for Tony Pulis' men.
Walters was full of praise for his side after they extended their unbeaten run to nine matches, telling Sky Sports 1: "We all work for each other, right from the back to the front. It was a full team effort from us today [Thursday] and a great win for us.
"We haven't conceded many this year, and to concede so early...but we've always got fight in us, and there was never any chance we were just going to lie down and take it.
"So from 1-0 down we showed great character to get back into the game and some good play from all over the team, especially the second half."
Stoke boss Tony Pulis said the way his side responded to their early setback reflected the confidence and character within the team as a whole.
"It was a great result and performance," he said.
"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."