The Blues took a first-half lead through John Terry's header, but the former England skipper was then stretchered off in obvious pain following an accidental collision with Luis Suarez.
Uruguay striker Suarez then equalised for the Reds in the 73rd minute, nodding home at the far post after Carragher had flicked on from a corner.
The veteran defender told Sky Sports: "I think in the first half Chelsea were on top but in the second we came out and great credit to the lads.
"We probably deserved a draw in the end, the way we battled in the second half."
It was Carragher's first start in the league this season and he said: "The Premier League is a step up (from the cups) with all its intensity and Chelsea is a difficult place to come.
"If I am picked I give everything; it is down to the manager, he is the boss."
When asked if not playing was frustrating, Carragher said: "Yes and no. I want to play but I understand. I am never going to cause a problem."
Reds team-mate Jose Enrique added: "Most important is the performance from the team. Suarez is an amazing player, a key player for us."