Rodgers was left lamenting his players' concentration levels and accused them of laziness after their 3-2 Europa League defeat to Udinese at Anfield on Thursday, in which the hosts took a deserved first-half lead only to concede three goals in 26 minutes after the break.
It was the latest setback in a mixed start to the season for the Reds which had just appeared to be gathering some momentum with three wins from the previous four games in all competitions.
Rodgers has no doubt his side can make great strides this term if they can improve at the back, but emphasised that he had been pleased with their attacking display against Udinese.
Reflecting on Thursday's match, Rodgers said: "We had been so dominant in the game and the players were outstanding, so I was just frustrated for them that we had let Udinese back in the game, and then ultimately come out of it with nothing.
"The players give everything and we are just working very hard to cut out the mistakes, because I think once we cut them out, we can be a real force as a team.
"The creativity in our team is improving every day and there is real excitement in the team going forward.
"If we can just cut out the mistakes that unfortunately we are getting punished for, then I believe we can do very well."
Liverpool are undergoing a transformation with Rodgers - appointed as successor to Kenny Dalglish over the summer - at the helm as they strive to improve on their disappointing recent run of top-flight finishes that has seen them come seventh, then sixth and last season eighth.
They are currently 14th in the table after six games, but Reds captain Steven Gerrard has been quoted as saying he thinks a top-four place is still a realistic goal for the campaign, and asked if that was something he echoed, Rodgers said: "Yes, absolutely - 100%.
"There is no doubt it is going to be very difficult for us, but that is our fight."
The manager, who was speaking on Friday at a press conference to preview Sunday's Premier League home clash with Stoke, added: "We have great quality here, the players are very much unified and there is a wonderful spirit in the group.
"Even though we are frustrated with last night's [Thursday] result, our performance in the league last time out (a 5-2 win at Norwich) was fantastic, so we will look to carry that into the weekend's game.
"There is still a very long season ahead of us, we are starting to get to grips with how we work as a team and I'm sure that will bring us good results."
Meanwhile, Liverpool have confirmed that defender Daniel Agger has signed a new contract with the club.
The 27-year-old Dane has made 177 appearances since signing from Brondby in 2006 and spoke of his delight about signing the extension, the length of which was not revealed.
"It means everything to me. This is where I want to be and I'm happy the club want me. I am really happy right now. I've never wanted to go anywhere else," he told the club's official website, liverpoolfc.com.
"I feel I am a part of this club - and I want to be a part of this club in the future.
"I like the way it is going right now with the style we're playing, and hopefully the results will come soon as well.
"The support from the fans has been unbelievable. The game when they were singing all the songs about me, it was difficult to focus on the game! It was such a good experience for me and I'd never experienced anything like it before.
"That is why I am so happy here. That for me is Liverpool Football Club.
"I feel I belong here and as long as the manager and the owners want me, I'll be here."