The 24-year-old opened the scoring for Chelsea from the penalty spot in the 40th minute, his fifth goal of 2026-27 so far.
Rogers’ good work was undone just a few minutes later, however, with Wesley Fofana conceding a spot kick and Cody Gakpo converting.
Fofana let the side down once again by missing the decider after the game went to penalties. Liverpool will now face Bournemouth in the next round.
Speaking to ITV Sports after the game, Rogers wasn’t happy, saying: "It is probably the worst way to lose a game.
"It was an even game and at times we had the better of it. I had half chances that I'd have liked to have put away.
"It was one of them that can go either way and you have to accept it."
