Peter Odemwingie bagged a hat-trick in the demolition, with Jonas Olsson and Keith Andrews also finding the net; Steven Fletcher scored a consolation for the below-par hosts.
Hodgson spoke of his delight after the victory and praised the players for their efforts.
“I think they deserve every credit,” The Hawthorns club’s boss told Sky Sports.
“We had to survive that harsh blow of an equaliser in added time of the first half, where really I thought we were looking very good value for our half-time lead.
“Everyone knows it can be a game-changing experience when you are coming in at half-time after playing well and you could be 2-0 or 3-0 up, but suddenly it is 1-1.
“I thought we really did well to go out and take the second half as we did the first half, and in the end we scored the goals and it was a very good victory, but it was down to the fact that the players played very well today,” he stated.
Mick McCarthy meanwhile is under added pressure after the heavy defeat, and has apologised to the fans for the performance.
“It is an understatement to say it has been a disappointing afternoon.
“It turned out to be a terrible afternoon, a disgraceful afternoon, in terms of our performance.
“We had weathered a (tough) first half and got back into it. We started the second half well and then failed to deal with two set-pieces, so we were 3-1 down and then we were caught on the break all over the place.
“It was an awful performance and, I don’t often do it, but I’ll apologise for that one to everyone who was here watching – our fans,” McCarthy concluded.
By Gareth McKnight