John Swift opened the scoring at Turf Moor with a stunning free-kick but the Baggies were pegged back soon after by Zian Flemming's equaliser.
It means West Brom have now been to Sheffield United, Leeds and Burnley and taken something, the latter two since Mowbray's return to The Hawthorns.
Reacting to Tuesday's draw in Lancashire, the boss said: "I'm trying to change the mentality of the players and I'm trying to get us to play on the front foot. I believe we can go anywhere and go toe-to-toe and have no inferiority complex.
"The best sort of defence is attack and playing in the opposition's half, as opposed to sitting back and trying to keep a clean sheet and letting the other team have a lot of the ball.
"I think the fans here want us to attack and play on the front foot. They want to see us score plenty of goals and win.
"I would rather win 4-3 than 1-0, if that makes sense. That's just my mentality. I want to win football matches and inspire the players on the pitch to fight for the badge.
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