Goals from Youssouf Mulumbu, James Morrison and Paul Scharner sealed victory for the Baggies, who have moved above their opponents in the battle for Barclays Premier League survival.
Hodgson said: "You look to do a job, try to prepare the players as best as you can - but at the end of the day it's all about players, not coaches. The players have got to do the job, and they can feel very satisfied coming away from a difficult match with important points at stake, having played so well from start to finish."
He added: "The board made the change of manager very late on. They realise a late change doesn't always work, and we still don't know if it will.
"But one hopes the confidence will improve with these results, and hopefully we have turned some sort of corner.
"There will be ups and downs, but hopefully there won't be so many blips that we can't get enough points to stay up."
West Brom striker Peter Odemwingie helped transform a below-standard opening 45 minutes after coming on as a second-half substitute for Marc-Antoine Fortune.
Hodgson said: "Fortune did well in the first half, running the channels and holding the ball up well, and I had a feeling the second half would be less frenetic and Peter would come into his own.
"I have not seen him play up front on his own before, but today he showed he can do the job."