Arkansas is now 2-for-2 for in the Triple Crown races.
Anthony said he knows Clinton, who seems headed for the Democratic presidential nomination, "very well," but declined to comment when he was asked if he's a Clinton supporter.
"This is a horse race," he said with a smile. He later added he was sure Clinton "was glued to a TV set somewhere."
Anthony is the owner of Loblobby Stable, which races approximately 50 horses and operates mainly in New York with a winter stop at Oakland Park in Hot Springs.
Anthony also is the chairman of the board of the Bank of Bearden in Bearden, Ark., and runs several lumber companies and timberland areas in the state.
His family settled in southern Arkansas in the 1830s and has operated lumber mills and farms and lived in that area for several generations.
"All promising Loblolly colts and some of the fillies are named for such places: creeks, valleys, bluffs, ridges, settlements, hills, crossroads, trails and swamps," he said.
Pine Bluff was bred at Longfield Farm in Goshen, Ky., near Louisville where Anthony keeps a broodmare band and Anthony made an immediate reference to that fact when he took the podium in the press room.
"A 502 horse finally won the Preakness. That's a Kentucky joke, most of the horses come from 606. This is the goal of a lifetime," he said.
Anthony is no threat to Jay Leno, but he was referring to the fact that 502 is the Louisville area code. The 606 area code is for the Lexington, Ky., area, which is noted for its horse farms.
This was Anthony's second victory in a Triple Crown event -- he won the 1980 Belmont Stakes when Temperence Hill -- and his first Preakness victory.
"Any time you win a classic . . . It's the hardest thing I've ever tried to get done in my entire life. It leaves you relieved, breathless and weak in the knees," he said.
Anthony thought his horse had a good chance when he started his stretch run.
"Coming down the stretch, I knew we were in position and I told my wife it's ours to win or lose from this point forward. [Jockey] Chris [McCarron] got every ounce there was in the horse, all that he needed certainly," he said.
Describing his emotions as Pine Bluff surged for the lead, "First, you're holding your breath most of the time. Whenever you can finally breathe, your heart is thumping so hard you can't hear the announcer. You see that you're still gaining on the horses in the lead and you know that you're doing well. Whenever you see that last step when the head finally nods over in front, that makes you proud to be an American, proud to be in Maryland and proud to own this horse."
Anthony said he didn't lose confidence in Pine Bluff when the horse finished fifth in the Derby.
"Confusion is a better word than loss of confidence. If he'd run a fifth and been beaten by someone other than Lil E. Tee, I would have lost more confidence, but we had beaten Lil E. Tee a couple of times so I thought well, hell, we've beaten the Derby winner twice, maybe we'd better go on and see if we can do it again," he said.
Anthony said he was pleased, but surprised his horse was favored in the Preakness. He liked the vote of confidence from the bettors for his horse.
"I think a lot of the logic behind why he was favored may have been a little faulty, but it does give you moral support to see people in the most important way of all putting their money down. That means maybe they knew something I didn't know," he said.