Daniel Sturridge netted his 14th league goal of the season in the 24th minute to give the Reds an early lead but they could not add to that advantage before Albion equalised with just over 20 minutes remaining.
Liverpool defender Kolo Toure misplaced a pass into the path of former Everton striker Victor Anichebe who made the most of the defensive error which was enough for the West Midlands club to snare a point.
After the match, Rodgers felt his side deserved to win and was only disappointed to see them not able to move four points clear of their fifth-placed Merseyside rivals.
"I thought that after the control we had in the first half, there wasn't many chances in the game, but I thought up until the mistake we made we were in control of the game," he told Sky Sports.
"Maybe we should have been 2-0 up but they pulled it back to 1-1. So it gives them a little bit of momentum and the game is in the balance.
"But it's a good point. We played some terrific stuff today, the pitch was awful conditions for a Premier League football pitch.
"We played some terrific stuff and created some good chances.
"Overall, I'm disappointed now that we haven't taken all three points but it's another point further for us in terms of where we're wanting to go."
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