Alderson told Mike Lupica on ESPN New York 98.7 FM there is "little to suggest it had to do with the no-hitter. He continued to pitch. He was symptom-free for a period of time thereafter."
Santana, who missed the 2011 season because of shoulder surgery, re-tore the anterior capsule in his pitching shoulder this spring.
Santana is leaning toward another surgery but definitely wants to attempt to resume his career, a source close to Santana's decision said Friday.
Coming off the injury in 2011, many questioned leaving the left-hander in for so many pitches, even with the franchise's only no-hitter on the line. Santana won three of his next five starts after the no-hitter, then lost his final five starts. His season ended in mid-August. He had an 8.27 ERA over the 10 starts after the no-no before landing on the disabled list.
Could making history ever be worth this kind of injury, Alderson was asked hypothetically.
"No," the GM said. "That wouldn't have been a price to be paid. Was [the no-hitter] a nice part of Mets history? Yeah, absolutely. If it came at the price of Johan's career? No, not worth it."
Earlier on Friday, Mets pitching coach Dan Warthen expressed confidence that Santana's 134-pitch no-hitter played no role in the probable re-tear.
"This is not a byproduct of the no-hitter," Warthen said. "At least I don't feel it was in any way, shape or form -- because he had good velocity and arm strength after that.
"And it doesn't matter, because he would have never let us get him out of the game anyway."
Warthen realized Santana was struggling this spring training, even if he didn't know the precise reason.
"He had trouble getting his arm into throwing position," Warthen said. "When he finally felt it was pretty good, the ball didn't come out like it generally does from Johan's arm."