The Baggies go into their clash with Arsenal at the Hawthorns just one point above the drop zone.
Hodgson has enjoyed a positive start to his reign at Albion, winning one and drawing three of his first four games since taking over from Roberto Di Matteo.
His side will have their work cut out to continue that unbeaten run for the next month, with matches against Liverpool, Chelsea and Tottenham to come in the coming weeks.
But the former Fulham boss is relishing the battle to beat the drop.
"I suppose the truthful answer would be yes, I'm enjoying it more now (than he did at Anfield) because no-one likes to be in a situation where the work you're doing is not appreciated," said Hodgson, who left Liverpool in January after a forgettable six months in charge.
"It's nice to be here where the work I'm doing is appreciated.
"But I've also got a sneaking suspicion that some of the work I did at Liverpool was appreciated by certain people."
West Brom go into their clash with Arsenal in the rare position of looking to complete a double over Arsene Wenger's men following their 3-2 win at the Emirates earlier in the campaign.
If that was a low point in the Gunners' season, the past few weeks have hardly gone to plan as, from fighting for trophies on four fronts, they have lost the Carling Cup final to Birmingham and been knocked out of the Champions League by Barcelona and the FA Cup by Manchester United.
Whether now is a good time to play them, or anything but, is open to debate.
"We don't think about whether they are wounded or not wounded, whether the results they have had have improved their play or made them weaker," said Hodgson.
"We just look at them as the very, very good team that they are.
"When you draw Barcelona in the Champions League, I don't care who you are, there's a risk you might not win the tie. And when you're drawn away to Manchester United in a cup game there's a risk you won't win that one either.
"I don't think those matches will affect at all the fact they are a very good team with very good players."
The only chance of silverware now left for Arsenal, who have not lifted a trophy since 2005, is the Premier League, but Hodgson rejects the idea Wenger has to win something this season.
"Of course I don't subscribe to that theory," he said. "I'm a football coach, I'm a football manager. Only one team can win the league.
"But if I was an Arsenal fan and I had had the chance to watch the football teams he's put together I'd be more than happy. So not only do I not subscribe to it but I find it offensive that it should be suggested."
West Brom are sweating on fitness of midfielder Chris Brunt ahead of the clash.
Brunt is suffering from a fever but Hodgson is hopeful he will recover in time, while Youssouf Mulumbu is fit to play after shaking off a muscle problem.
Graham Dorrans is definitely out with an ankle injury, while on-loan striker Carlos Vela is not eligible to face his parent club.
Jens Lehmann hopes some of his 'Invincibles' aura can rub off on Arsenal's young squad as they look to finish the season on a high by finally landing the Premier League title.
The 41-year-old has rejoined his old club on a short-term monthly rolling contract to aid an injury crisis after Wojciech Szczesny joined Lukasz Fabianski and Vito Mannone in the treatment room.
Lehmann is set to provide experienced back-up to Manuel Almunia, whom he duelled for the number one jersey before leaving in 2008, and will be on the bench at West Brom.
The former German international certainly brings plenty of kudos with him - having played in every one of Arsenal's 38-match unbeaten run to the title in 2003/2004 as well as lifting the 2005 FA Cup and helping the team reach the Champions League final in the following season, where he was famously sent off after just 18 minutes.
"I have got that - in terms of experience, I am still good, so I need to give that onto the young lads," Lehmann told Arsenal TV Online.
"I hope we will be successful in getting the trophy, to give that extra bit of conviction to the players - that is why I am here and why the boss has asked me to come."
Source: DSG
