Liverpool and Everton played out a classic Merseyside Derby, with the visitors snatching a draw after super-sub Daniel Sturridge’s last-gasp header.
“We should have gone 3-1 and that would have killed the game. After that we couldn’t keep ball,” Reds boss Rodgers said. “I’m disappointed with the defending from the corner and we have to be stronger. All-in-all a wonderful game and when you come to your rivals it is important not to lose.
“We again showed our resilience and ability to fight back. This is a difficult place to come and they haven’t lost at Goodison Park this year.”
Philippe Coutinho gave the Reds an early lead but Kevin Mirallas put the hosts back on equal terms soon after.
Luis Suarez restored Liverpool’s advantage before half-time with a stunning set-piece strike which he powered through the Everton wall.
The Toffees, though, kept pressing and Romelu Lukaku drove home their second on 72 minutes before putting them ahead 10 minutes later, heading in a corner.
But in what was a fitting result Sturridge rose to head Reds skipper Steven Gerrard’s free-kick beyond keeper Tim Howard in the dying minutes.
And Everton boss Roberto Martinez was frustrated with his side’s poor defending.
“It’s really disappointing we didn’t get three points. I’m disappointed to concede from three set plays,” he said.