Rodgers' men have now lost two on the bounce, falling from first place on Christmas Day to fifth heading into the New Year.
However, Rodgers was happy with their efforts in challenging away games against Manchester City and now Chelsea and remains confident his side are in the title frame.
"I thought it was a great effort by my players," he said. "We've had two really tough fixtures against two of the strongest squads in the Premier League.
"To get them back-to-back at this time of year was always a big ask and with so many injuries as well. To keep the game in the balance to the very end, you have to give credit to the players.
"Of course we're disappointed but right now I'm more worried about the group, we're nursing injuries and we'll see where we are tomorrow."
Liverpool lost Joe Allen, Mamadou Sakho and Glen Johnson to injury at Stamford Bridge and Rodgers will be hoping to patch his squad up for Wednesday's visit of Hull City.
Rodgers, in trouble with the FA for his remarks after the loss to City, praised referee Howard Webb's overall performance at Stamford Bridge but said goalscorer Samuel Eto'o was lucky to be around to score the winner after an early challenge on Jordan Henderson.
"He was very fortunate even though it's so early in the game," he said. "Howard was excellent today but that was a poor challenge. I know we scored from it but he's raked his studs down the leg and shin and I'm surprised he didn't get a card.
"He (Eto'o) should've been sent off. I know we scored from it, but that was a wild challenge, where he's raked down his knee and down his shin and didn't even get a yellow card."
Chelsea boss Mourinho sought to take the blame, saying he had told Eto'o to take a more physical approach.
"I didn't see it, I don't know which situation you are referring to," he said when asked about the challenge on Henderson.
He then added: "For some weeks I have been criticising him a lot internally for his failure to adapt to what the Premier League is in terms of physicality so if he had a tackle deserving of a card it was my fault because I'm asking him to adapt to this."
Rodgers had a number of youngsters on the bench with injuries biting, and admitted reinforcements might be needed in January if they are to keep their title challenge alive.
"I think that's always been the case," he said. "The squad is very shallow.
"It shows the size of the challenge that you can lose two games and go from top to fifth but I'm confident if we can get some players back and maybe add one or two more we can be well set.
"We've already shown we can be a team that is exciting to watch with confidence and creativity, and we've still got improvements to make."