Late goals from Gareth McAuley and Romelu Lukaku secured a shock win for the visitors after the Reds had dominated the contest throughout but were ultimately left frustrated by an outstanding display by Ben Foster.
The Baggies goalkeeper kept Liverpool at bay with a string of saves, including a 77th minute penalty stop from Steven Gerrard in front of the Kop.
“The players gave everything in the game,” Rodgers reflected. “After all the shots and attempts at goal, we just couldn’t make the breakthrough — and the longer it goes on, it gives the opponent that wee bit more encouragement.
“But I can’t fault the players. I thought they gave everything tonight — it was just one of those games where we needed that first goal.”
In total, Liverpool had 25 efforts at West Brom’s goal, with seven on target.
“The players gave everything,” Rodgers added. “We weren’t at our best tonight, but we were certainly on the front foot and looking to create.
“It was a good away performance from West Brom — if you come, defend and keep the score at 0-0, you’re always in with that chance.
“Ben Foster made some brilliant saves tonight that kept them in the game.
“I’m disappointed for the players. They’ve been on a terrific little run, especially here at home.
“We’ve defended very well throughout the season here and we’re disappointed with the [first] goal. The second goal was one where you’re chasing the game and you get caught on the counter attack, and he’s put it away well.”
The award of a penalty 13 minutes from time after Jonas Olsson had pushed Luis Suarez inside the box gave Liverpool a chance to take a well-deserved lead.
However, Gerrard saw his low effort turned away by Foster.
“It looked from the side that it [the penalty] may have been a bit harsh, to be honest, but I haven’t seen the replay of it,” Rodger said. “The referee has given it and it was an opportunity for us, but there is no blame on Steven. He’s been outstanding and hasn’t had many penalties to take [this season]. Again, he was very, very good tonight and it happens. He’s got the courage and bravery to step up, but Ben Foster has made a good save.”
Liverpool return to action on Thursday evening with a trip to Russia to take on Zenit St Petersburg in the first leg of the UEFA Europa League last 32 tie, before playing host to Rodgers’ former club Swansea at Anfield on Sunday.
“It’s a big disappointment because we had two home games this week that we felt were opportunities for us,” Rodgers concluded.
“But we’ll go again and get back in tomorrow. We’ve got a game away in the Europa League which we’ll be ready for on Thursday and then come back, get ready and go again at the weekend.”