Albion were beaten 2-1 by Norwich at The Hawthorns Saturday, which cut the gap between themselves in 15th and the Barclays Premier League drop zone to five points.
It was West Brom's third straight loss in the league and seventh in the 11 top-flight fixtures at their own ground this term, during which they have managed to score just eight goals.
That record is concerning Hodgson, who said: "I've had lots of times in my career when I've had long runs of away defeats, but I don't know if I can remember seven home defeats.
"It is a very negative statistic. If we are going to survive in this league and get to where we want to be, we need to take points at home and once again we have failed to do so."
Asked if he felt his side were in a relegation fight, Hodgson said: "We have been in that for a long time, and will be in it for a long time to come.
"There are a lot of teams in it because all you need is a couple of bad results and then you are dragged right down there."
He added: "The morale is nowhere near as high now as it was last season when we were winning games, or not getting beaten.
"But it is a very common dilemma and one which comes about because we are in a result-oriented business.
"Every time you are not winning, everyone at the club is unhappy. It is as it is and we will have to deal with it."
West Brom, who had not netted in their previous three league matches, went close in the first half, with Peter Odemwingie's shot being tipped on to the bar and James Morrison having an effort cleared off the line, only for Andrew Surman's volley to then hand Norwich the advantage in the 43rd minute.
Fit-again Shane Long came off the bench and equalised with a penalty in the 68th minute following Daniel Ayala's foul on Jerome Thomas, bringing Albion's goal drought to an end.
It was not enough to salvage them a point, though, as a Canaries breakaway 11 minutes from time saw Steve Morison nod in the winner from a Grant Holt cross.
Long, who returned to action after being sidelined recently by a back problem, feels the Baggies have not been playing better than results would suggest at home but need to start making it count.
"I think in a lot of the games we have played well," Long told Albion Player.
"We are losing to teams around us, which is not helping us, and if you look at the likes of Wigan and Stoke, there are a lot of games there that we should not have lost.
"But just a sucker blow at the end and that's it - the points are gone. It is something we have to learn from.
"We are halfway through the season now, but we have got a long way to go still and hopefully if we keep playing well, we can start turning performances into results."
It was a second consecutive away win for Norwich, who remain ninth in the table and have amassed an impressive tally of 28 points from their 21 Premier League fixtures since winning promotion to the top-flight last summer.
They are still looking for their first clean sheet of the season, but when asked if that worried him, Canaries manager Paul Lambert said: "It would do if we weren't winning games.
"We gave away a penalty, but the most important thing is that we are winning.
"That is the nature of the beast - you just have to try to win more games than not, and the group have certainly done that.
"It would be nice to walk away with a clean sheet and the lads are desperate for it, but we are winning games."
Meanwhile, Lambert revealed that goalkeeper Declan Rudd, who was replaced in the team by first-choice stopper John Ruddy having played in last weekend's FA Cup win over Burnley, could be facing a couple of months out after injuring his ankle.