The Reds were dominant for the majority of the Anfield contest, creating 19 shots on target, and were hit with a sucker-punch when Gareth McAuley nodded in the opener with their first meaningful attack.
It closely followed a penalty miss by Steven Gerrard for the hosts and, with Romelu Lukaku scoring a late second to rub salt in the wounds, Rodgers told Sky Sports: "The players gave everything. It was just one of those games with all those shots that we couldn't make the breakthrough.
"We've been on a terrific run. I'm very disappointed with the goal. That first goal was crucial.
"I can't fault the players, though. We weren't at our best but we were on the front foot for most of the game. It's a good away performance from West Brom.
"If you can keep it to 0-0 you always have a chance. And Ben Foster has made some fantastic saves to keep them in the game. Losing is a big disappointment but we'll be back in tomorrow and get going again."
And on Gerrard's saved spot-kick that turned the game in West Brom's favour, Rodgers added: "He's got the courage to get up and take it. There's no blame. It was a good save."