The Elizabeth Taylor and Richard Burton biopic was roundly criticised when it aired late last year, with TV Guide calling the movie "laughably inept" and suggesting that Lohan was miscast.
Bowler appeared at the TCAs this week to promote his new series Defiance, but also spoke about the backlash against Liz & Dick.
He told Access Hollywood: "[The reaction to Liz & Dick] was disappointing in a way because everybody worked so hard. We had an Oscar-winning hair team, we had an amazing make-up team, the wardrobe was sublime.
"You work as hard as you can and you try your absolute best, but you never know the end of something at the beginning of something. That's the luck of the draw and that's the game."
The production of Liz & Dick was the subject of controversy, with Lohan's legal problems allegedly delaying filming on multiple occasions.
Bowler even admitted in November that Liz & Dick's erratic shooting schedule was at times frustrating.
"There were exercises in patience and there were exercises in tolerance," he explained last year.
"I believe it could have been smoother at times, it could have been a lot smoother at times and we could have got a lot more done on a couple of days, but you get what you're given."
Liz & Dick drew 3.5 million viewers in its initial airing, which was less than network Lifetime had expected.