Swansea started with a bang as Belgian winger Roland Lamah put them in front after less than two minutes, beating Steven Reid on the by-line before curling the ball past England international Ben Foster.
The Baggies took hold of the game in the second half and Congolese midfielder Youssouf Mulumbu's side-footer from 20 yards nabbed the much-needed three points after Stephane Sessegnon levelled from outside the box on 53 minutes.
Monk said: "You never have it won by half-time, whatever game you play in. The way we played first half was pretty much exactly how we wanted them to play.
"They carried it out, we were getting crosses, we were causing problems, we were getting chances and probably could have taken a few more, so probably should have taken more from the first half.
"You've got them on the ropes and if you don't knock them out, you're always open to them coming back into the match and that's exactly what happened. (It was a) very good first half and very poor second half.
"The way we come out second half was very sloppy, very poor. Our passing was poor, our touches invited West Brom onto us and then unfortunately the second goal in these sorts of games is always crucial.
"They got the second one, which gave them the impetus going forward and unfortunately we conceded a second. I don't think we deserved to lose the game, but we definitely didn't deserve to win it after that second half performance."
- Sports & Recreation