Speaking to The Athletic's Lindsey Adler, Stanton called it "a terrible moment."
"You never want to see your teammate on the ground, especially by the hand of yourself," he said.
There was immediate concern when Stanton hit a ball that caromed off Tanaka's head. The Yankees pitcher fell to the ground, and coaches and the medical staff went out to look at him.
Tanaka tweeted Saturday evening that he was "feeling it a bit right now, but I'm all good."
Yankees manager Aaron Boone told reporters that Tanaka was diagnosed with a mild concussion: "I think all the signs are pointing that he really dodged the bullet there. We're encouraged where he is, but we'll take it day by day. Hopefully it's not something that's too long."
Boone was unable to say if Tanaka, who is in MLB's concussion protocol, would be available for the start of the regular season.
Tanaka is entering his seventh campaign with the Yankees. The two-time All-Star posted a 4.45 ERA and 149 strikeouts in 182 innings last year.
New York will open the 2020 season July 23 against the Washington Nationals at Nationals Park.