Rodriguez, 38, connected with an R.A. Dickey knuckleball in the fifth inning of the Yankees' 5-2 loss to the Blue Jays on Monday at Rogers Centre, but he left the stadium without speaking to reporters.
With a day to ponder the milestone, Rodriguez said that there was still not much to say about it.
"It's hard to reflect on it right now," Rodriguez said. "We're in the middle of a pennant race, and we need wins like oxygen right now. I think at some time, there will be a time and a place to appreciate that. But it's probably not right now."
Yankees manager Joe Girardi acknowledged that Rodriguez's appeal of a 211-game suspension and the corresponding allegations of performance-enhancing drug use could be one explanation for why Rodriguez's 650th home run did not seem to be celebrated.
Girardi also noted that milestones with numbers in the hundreds tend to be more publicized.
"My thoughts? I haven't seen where 50s have been celebrated," Girardi said. "Hundreds have, or maybe when you pass a guy who's in front of you. It's not every day you see someone hit 650, but it seems like the hundreds are the ones people concentrate on more."
Rodriguez ranks fifth on baseball's all-time home run list and is gaining ground on Hall of Famer Willie Mays (660). Rodriguez's Yankees contract includes a $6 million bonus payable if he ties Mays.
"I can't really think about that right now," Rodriguez said. "Really, we need every victory right now. We need every game. That's my focus, and I've got to try to go out there and help my team win."
Bryan Hoch is a reporter for MLB.com. Follow him on Twitter @bryanhoch and read his MLBlog, Bombers Beat. This story was not subject to the approval of Major League Baseball or its clubs.