Tepesch, called up from Triple-A before the series opener, lasted just four innings and was ineffective, allowing five runs on seven hits, suffering the loss after the Dodgers couldn't climb out of an early hole, down 4-0 in the second inning.
He faced 19 batters in his first major league start since 2014.
"When he got to two strikes, he left some pitches up, and they took advantage of it," manager Dave Roberts said. "Nick gave us what he had, but third time through, seeing those guys, I thought that was enough for him."
"I just made some bad pitches up in the zone and they took advantage of it," Tepesch said. "I had some counts where I was ahead and I didn't make good pitches, and it hurt me."
Roberts didn't rule out Tepesch making another start, which would likely be Wednesday in Milwaukee, though a decision could be made much earlier than that.
"Nick's made 40 major league starts and performed in Triple-A for us," Roberts said. "I think we're going to decide here tonight or tomorrow morning what's best for our club going forward."
Tepesch had a 3.36 ERA in 14 starts in Triple-A this season between Round Rock and Oklahoma City, and lasted at least five innings in 13 of those 14 starts, including at least six innings eight times.
"I'll do my work each day and get ready for my next start," said Tepesch, unsure of where his next outing might be.
Dodgers starting pitchers not named Clayton Kershaw are averaging 5.04 innings per start in June.
"You've got to rely on your starters, you have to," Roberts said, "I know that, and I know the starters know that and outside of Clayton, I know they know that, so I think that those guys have taken this challenge upon themselves.
"These guys are giving what they've got but yeah, we've got to get length from our starters consistently. I think anything outside of that is not a formula to sustain itself, or to sustain winning, I'll leave at that."
The Dodgers and Pirates are back at it again on Saturday in a nationally televised game on Fox, at 4:15 p.m. PT. Kenta Maeda takes the ball for the Dodgers, against left-hander Jeff Lock for Pittsburgh.