Roy Hodgson, the West Bromwich Albion manager, thanked the Liverpool supporters for the reception he was afforded during his team's smash-and-grab 1-0 win on his return to Anfield yesterday.

Peter Odemwingie's goal 15 minutes from time earned Albion three points – their first win at Anfield for 45 years – on Hodgson's first return to the ground since being sacked in January 2011 after six months in charge.

Hodgson said: "It really was a magnificent rearguard action and the other great satisfaction for me today, of course, was the support I got from both sets of fans. I was a bit concerned coming back here. Everyone said 'you'll get a decent reception' and I was really pleased they treated me so well.

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"Obviously, I didn't repay them too well by coming away with a victory but it was nice that both sets of fans gave me the reception that I was hoping for."

Liverpool dominated the match but still dropped yet more points at home. Had they converted all their chances, they would probably have made it into double figures but their season-long scoring problems cost them dear once again.

Kenny Dalglish, the man who replaced Hodgson, will be wondering what his side have to do solve their problems in front of goal after twice hitting the woodwork and having a penalty claim rejected, in addition to numerous other opportunities.

But having not broken West Brom's resistance, there was always the risk of punishment and it was duly delivered by Odemwingie in the final quarter of the game.

Liverpool have now won just one Barclays Premier League game at home in 2012 and scored only six goals in seven matches, and have dropped 27 points at Anfield in the current campaign.

With diving back on the agenda after recent incidents involving Manchester United's Ashley Young, the spotlight was on Maxi Rodriguez in the most contentious incident of the first half. The Argentine did appear to be caught by Billy Jones as he flicked the ball past him on the edge of the six-yard area but referee Neil Swarbrick waved away penalty appeals.

Liverpool, without the injured Steven Gerrard, should not have had to rely on the official for a helping hand after a number of chances went begging.

Their previous nine draws and two defeats at home were a direct result of them failing to convert and the first half was almost a rerun of games gone by.

Players seemed to be queuing up to squander opportunities as dominance in possession failed to lead to an end product.