Arch-rivals Rangers, meanwhile, have been grinding out matches of late to extend their advantage at the top of the table.
Former Hibernian and West Brom manager Mowbray claims he is trying to give Celtic an identity worthy of the club's heritage but insists he would not snub a more direct approach if the situation warranted it.
"For long-term success, you've got to carry a footballing philosophy through your football club," said Mowbray, whose side have drawn their last two SPL games.
"The players must know what is expected and know the demands put on them every day in training and every day out on the field.
"You don't throw that all in the bin if you draw a couple of games or you lose a football match.
"I like to give my teams an identity and I think I've done that in the past.
"I think the Hibs team and West Bromwich Albion team were known as as good a footballing team as there were in the division that they played in.
"West Brom still carry that along now.
"I watched them this week and the commentator was constantly talking about this great passing game.
"I'd like to think that was put down by ourselves at West Brom over this three-year period and that stays and sticks.
"I'm trying to do that here."
Celtic could find themselves 12 points adrift of Rangers by the time they take to the field at St Johnstone on Sunday.
Mowbray added on the Hoops' online television channel, Channel 67: "The heritage and history of this club is that they've tried to be entertaining, attacking, open, flair football teams.
"I haven't got a magic wand to change that overnight.
"It is the balance of winning titles, as the club have done over the last few years, of course.
"But getting that balance of winning and entertaining as well at the same time and that's the process we're going through.
"That said, in any 90 minutes, when you need to go direct in the last 10 minutes of a game and you need a goal and you have a big 6ft 3in centre-forward, you put the ball in the box.
"I don't ever blindly stick to principles that we must pass, pass, pass right to the death.
"We play to win, of course."
Scottish Premier Winner 2009/10 Win Outright: Celtic 2/1