Emre Can's first goal since his summer move from Bayer Leverkusen put Liverpool in front, before Gary Cahill's equalizer and Diego Costa's 10th league goal of the season clinched victory for Chelsea.
But Rodgers was lefty fuming by Taylor's decision not to point to the spot late on when Steven Gerrad's shot appeared to strike the arm of Chelsea defender Cahill.
"The technology coming into the game has been great: sometimes it goes for you, sometimes it works against you," he said.
"It is bitterly disappointing for us that there was a big decision in a big game that we didn't get.
"It was a clear handball - and you need to get that. If we weren't going to get it (a goal) from open play we should have got it from the penalty spot.
"The referee had a clear look at it but he maybe needed some help from his linesman."
The result means Liverpool have lost three games in the space of a week after Tuesday's loss to Real Madrid and last weekend's defeat at Newcastle.
Rodgers made seven changes for the game against Los Blancos at the Bernabeu but the Liverpool boss has no regrets about his team selection for the last two matches.
"I would hopefully win the three games," he said when asked what he would do differently.
"We plan and prepare the team the best we can so I wouldn't do anything different, we just didn't get the results.
"Hopefully this will be an experience for us this week and we can use that to be better going forward."