But manager John Gibbons sees the 28-year-old right-hander getting another shot.
"I don't see why not," Gibbons said. "I thought he did a solid job. He gave up a few solo home runs but I thought he was aggressive. He attacked. He seemed to settle in as the game went along. He started to get his breaking ball over a little better."
Beyond Marcus Stroman, J.A. Happ and Marco Estrada, the Blue Jays have two rotation spots to fill for the remaining 49 games. Cesar Valdez filled in with varying results before recently landing on the disabled list, and Joe Biagini is getting stretched out with Buffalo and could need a few more starts before returning.
A year after Toronto needed just seven starters, Tepesch is already the 11th of 2017. He underwent surgery for thoracic outlet syndrome in '15 and has bounced around since being released by the Rangers in '16, so with the potential of another start in Toronto, Tepesch is hoping to keep the door propped open.
"I'm just trying to take advantage of the opportunity," Tepesch said. "Just go out there, try and improve on this one, and get better each time I take the ball whenever they decide to hand me the ball."
The Blue Jays also need a starter for Saturday, and beyond Tepesch, their upper Minors depth is thinning. Chris Rowley, Brett Oberholtzer and TJ House are options at Triple-A, while left-handed prospect Ryan Borucki is pitching well in Double-A and already on the 40-man roster, but his inexperience and schedule make that highly unlikely at this point.
What makes this rotation churn difficult for the Blue Jays isn't just the quality of pitching, but the number of innings coming from their starters. They burned through six relievers Wednesday, and as a group have thrown more innings than any other bullpen in the American League. As the depth of that group is tested, too, the importance of these starters becomes even clearer.
"We didn't have a whole lot left down there," Gibbons said. "Our bullpen guys have been getting abused a little bit, so that's what happens. I made the decision to take Tepesch out when I did. I could have gone with maybe one or two other guys a little longer, it might have covered us a little bit."