The Reds dominated large periods of the match, with the Baggies only registering their first shot in the 80th minute. However, they scored twice in the final 10 minutes to claim all three points, leaving Liverpool to rue a string of missed opportunities.
Rodgers admitted that his side were not at their best, but believes that the number of chances created was a positive.
"The players gave everything into the game," said Rodgers.
"We just couldn't make the breakthrough and the longer it goes on, it gives them a wee bit more encouragement. I can't fault the payers. I thought they gave everything tonight. We just needed that first goal.
"We weren't at our best but we certainly were on the front foot, looking to create."
The result sees Liverpool drop to ninth in the Premier League table, while West Brom replace them in eighth.