The Reds dominated at Anfield - Steven Gerrard having a penalty saved by Ben Foster - but were stung by goals in the last nine minutes from Gareth McAuley and Romelu Lukaku.
That ended a run of three successive home victories, in which they had scored 12 and not conceded, and came after encouraging back-to-back draws against Arsenal and Manchester City in their previous two matches.
With the confidence bubble burst and hopes of a top-four finish in tatters, trailing Tottenham by 12 points with a dozen games remaining, Henderson believes a return to European action can provide an important boost.
"We just have to keep going, keep our heads up and bounce back from this," the England international said ahead of Thursday's trip to face Zenit St Petersburg.
"We just have to stay positive and think about the next game now which is Zenit in the Europa League on Thursday night.
"We know the European game is important as well but I think every game is important to be honest.
"We will keep improving and make sure we keep going in the right direction.
"Hopefully we can improve, get some better results in the league and look to close that gap.
"We have to take each game as it comes and play well every week and hopefully we will get better results than last night."
West Brom arrived at Anfield with a gameplan to press and stifle and they achieved that to a greater extent, although they were indebted to Foster for a string of saves to keep the scores level.
Liverpool missed the cutting edge provided by £12million January signing Daniel Sturridge, who was sidelined with a thigh injury after scoring four goals in six appearances.
"Daniel is a quality player and everyone has seen that since he's come in," added Henderson.
"You obviously miss good players and that was the case.
"We're all very disappointed. We had a few chances in the game but we just couldn't take them.
"We just have to stay positive and concentrate on the next game.
"The manager didn't have much to say after. We all know we didn't play particularly well but we have to move on.
"I don't think we passed the ball as well as we could have done. We didn't play particularly well.
"We had a lot of the ball but we didn't create as much as we have been doing.
"It's a game we could have won but it just wasn't our night.
"It's frustrating but that's football. You have to take these things on board and learn from it."
Forward Fabio Borini is looking for a personal boost from the Europa League having struggled to get up to match sharpness after his return from a broken foot in recent weeks.
The Italian has made just one start - in the shock FA Cup defeat at Oldham - and three substitute appearances but is likely to be given a chance in Russia.
His only goal in 15 appearances since arriving for £10.5million from Roma in the summer came in August's Europa League qualifier against Gomel.
Borini feels he has benefited from gaining European experience and hopes to build on that further.
"It has been very helpful to my career," he said.
"I played a couple of games in the Europa League before I got injured and it has been really good because it is a different way of football to the Premier League.
"You have to be organised. You have to take care of not conceding first and then you think about scoring because not to concede away goals is important."