"Obviously, big picture, that's quite an honor to tie Reggie," Rodriguez said. "I'm sure Mr. October is going to have a lot to say about that."
Rodriguez hit the solo shot off Braves starter Derek Lowe in the top of the first inning, with his first swing sending the ball over the 400-foot marker in center field to give the Yankees an early 2-0 lead.
A-Rod finished the evening 3-for-5 with four RBIs and two runs scored, saying that he expected to have messages from Jackson waiting for him at some point.
"I haven't checked, but I'm sure there's going to be multiple," Rodriguez said.
Jackson expressed some of his feelings about Rodriguez's pursuit in a Feb. 25 chat with reporters, acknowledging that Rodriguez would soon "blow by me like I'm standing still."
Jackson chuckled at that comment, but the Hall of Fame slugger said that he also has a problem with players who played in the era of performance-enhancing substances surpassing him on hallowed lists.
Six players have now hit the 563-homer mark since Jackson's retirement, though among them, only Rodriguez has admitted to using performance-enhancing drugs.
"I guess I get angry sometimes," Jackson said then. "I've been reprimanded by the Commissioner [Bud Selig] and the president of our team. I pleaded with them to say, 'Try to understand. I'm personally involved. I'm selfish today and made some negative comments.'
"I'm hurt and bewildered. I don't know if we'll ever get through it. We're all hurt, and it's in our lifetimes."
Asked Thursday if it is awkward for him to pass players like Jackson, Rodriguez replied, "No, not at all. Just happy to be playing baseball."
The homer, Rodriguez's 10th since returning from the disabled list on May 8, also ended a 69-at-bat road homerless drought for the slugger, his longest streak since June 25-July 25, 1997.