The Baggies sealed the title at the weekend, helped by their three wins and three draws last month.
"The Championship has been an unusual league this season and nobody has been able to pull away at the top and right to the death it was a bit like that," Mowbray told Sky Sports News.
"Going into the last month we had seven games and five of those seven games were away from home and it was a daunting task for us.
"But credit to the players they dug deep and their quality came through in the end. I trusted the team and our ability to score goals in this league and to be fair they come good."
Colin Calderwood, the Nottingham Forest boss, was honoured in League One and the MK Dons boss Paul Ince took the prize for League Two.