Late goals from Gareth McAuley and Romelu Lukaku - after a string of saves from goalkeeper Ben Foster, including a Steven Gerrard penalty, had kept the Baggies in it - saw them leapfrog their opponents into eighth.
Rodgers did not attend the post-match press conference, opting only to fulfil his obligations to broadcasters covering the game. "It was one of those games we couldn't get the breakthrough," he said.
"The longer it goes on it gives the opposition more encouragement. It's a big disappointment because we had two home games this week (the other is his former club Swansea on Sunday) that we felt were opportunities for us.
"But we'll go again and get back in tomorrow. We've got a game away in the Europa League (against Zenit St Petersburg) which we'll be ready for on Thursday and then come back, get ready and go again at the weekend."