Oswalt met with manager Ron Washington on Tuesday to discuss what happened on Sunday and also explained his situation with reporters before the Rangers' game with the Red Sox.
Oswalt said he threw 96 pitches in a start against the Angels on July 30. He then threw 50-60 pitches in a bullpen session on Wednesday in anticipation of starting on Sunday. Instead, the Rangers moved him to the bullpen.
The veteran made his first relief appearance against the Angels on Thursday, throwing 24 pitches in two innings. He threw 30 pitches over two innings against the Royals on Sunday and then said "that was probably enough" when asked if he could keep pitching in a tie game.
"Now you're talking about being in the 200-pitch range in a week," Oswalt said. "There's not many pitchers that do that. Another one or two innings and you're talking about being around 250 pitches.
"That's when they asked me and I said I probably had enough. I'm trying to do my role. I've never done this before and I'm still learning. I just want to try and do my role and stay healthy."
Oswalt said he still wants to be a starter, but he is willing to accept the bullpen role right now and pitch whenever the Rangers need him.
"I'm down there until they say something else," Oswalt said. "I still consider myself a starter. If you asked anybody who has been starting for 10-12 years, they wouldn't be happy with moving to the bullpen. If they were, they're not competitors. But I'm in the bullpen, I'll throw down there and see how it goes."
Oswalt said Sunday's misunderstanding most likely came from the Rangers not accounting for the number of pitches he threw during his bullpen session last Wednesday.
"That's a very fair statement," Washington said.
Of his meeting, Washington said, "We had a chance to clear the air. It wasn't like we had to clear the air of something negative. We just had to clear the air of what we said and we moved on."
Oswalt said he has not asked the Rangers to trade him to a team that would allow him to start.
"I haven't said anything like that," Oswalt said.