The Red Bulls conceded to Julio Morales just prior to the half-hour mark before Tim Cahill answered for the Red Bulls but Chivas managed to score two more times through young gun Erick Torres.
Dax McCarty gave the Red Bulls some hope with a late goal but the damage had been done, leaving Petke to try and come up with an answer as to how his side were beaten despite dominating proceedings in the first half.
"I'd probably be coaching Barcelona next year if I could answer those questions every week. I don't know," Petke told reporters when quizzed on the reasons for the loss.
"We had many opportunities, especially in the first half, could've been up 3-, 4-nothing in the first half. No disrespect to Chivas, they're definitely in a rebuilding year, so just no disrespect, but we're a much better team than them.
"But this is MLS, and again the parity issue is proven -- that any team could win on any day. And they come in today and they got the goals, and we didn't. Credit to them."
Petke later added: "I apologize for that loss. We lost to one of the worst teams in the league. We had many chances, we didn't capitalize on them, made some mistakes and had no creativity in the second half. We looked like we were confused out there."
The defeat left the Red Bulls third on the Eastern Conference table as Chivas remained bottom in the West.