Mowbray said: "I'm delighted for the players and the staff. It's been a long, hard season after the play-off final defeat and the changes in the squad during the summer.
"We had the expectation of people saying 'Albion are the best team in the league' to deal with. That could have been a burden but full credit to the players for overcoming that.
"We're almost there and it will take a strange set of results at the weekend to deny us promotion but the players in the dressing room were already talking about winning the league.
"That was a strong feeling amongst them after the final whistle. I enjoy winning any match. I am not outwardly emotional but inwardly I enjoy things as much as anyone else.
"I will enjoy the moment when I get home with the family. Then I will feel the warmth of getting into the Premier League."