The draw extended the Reds’ winless run to four matches, leaving pressure mounting as they sit 14 points behind league leaders Arsenal.
Florian Wirtz gave Liverpool the lead with his fourth goal in six games, seemingly putting them on course for three crucial points.
However, Burnley fought back, with Marcus Edwards scoring his first league goal of the season midway through the second half, securing a valuable point for the Clarets in their fight against relegation.
"That won't be acceptable – a draw with Burnley at home, with all due respect," the Liverpool hero said on TNT Sports.
"If you're being critical of the Liverpool team - even though they're on a better run in terms of unbeaten games – the draws to the likes of Leeds and Burnley at home. That's not acceptable.
"There will be a lot of criticism that comes the manager's way again. But give the manager credit. The last time we spoke about this, you asked me if the team was in a crisis, and I said I didn't think it was in a crisis because I felt like this manager was capable of making things better and steadying the ship.
"He has moved the team from the middle of the table and up back into the Champions League positions.
"I think that will be a priority for him and the team, minimum top four this season, but that won't take anything away from the criticism that will come his way."