Rivera, 42, said that he has been given blood thinners to dissolve the clot and that it will not affect his recovery from the torn right anterior cruciate ligament and meniscus in his right knee.
"Maybe it is a blessing; I always see it like that," Rivera said. "I always say that things happen for a good reason. I was more concerned with the blood clot than the knee.
"For a minute, I was like, 'What else can happen?' To me, it's a blessing. I didn't ask why it happened, I didn't ask how it happened. I asked, 'How do we deal with it?' That's the way I wanted to leave it."
Rivera spoke to reporters on Wednesday at Yankee Stadium, walking with the use of crutches. He said that he noticed a stiff and sore sensation in his calf during the examination of his knee, mentioning it to the attending physician.
While the Yankees seem confident that Rivera will be able to return from the knee injury, the all-time saves leader said that the surgery has not yet been scheduled because he needs about two weeks to strengthen the knee.
"I believe [the clot] is taken care of already," Rivera said. "I trust the good Lord. Now I have to just strengthen it and be ready for surgery. This is the first time that I have to do something like that, that I have to strengthen part of my body to go to surgery. I have to do it; I have to have full range of motion, and that will be better for the surgery."
One day after Rivera suffered the injury while shagging batting-practice fly balls in Kansas City, the all-time saves leader vowed to return to a big league mound in 2013, saying that he did not want his career to end on the warning track at Kauffman Stadium.
Rivera revealed on Wednesday that he had been leaning toward pitching in 2013 even before the injury, despite the fact that he strongly hinted in Spring Training that he was considering retirement.
"I was leaning toward coming back; I was feeling strong on that," Rivera said. "It's hard. I was weighing how I feel, the traveling, the games, and it's the same. The traveling, I hate it. The playing, I love it. I was torn between that."
After being discharged from the hospital, Rivera said that he watched Tuesday's 5-3 Yankees victory over the Rays on television and was screaming at the screen, urging David Robertson to succeed in Rivera's vacant ninth inning.
"I was home, right on the couch," Rivera said. "I was sweating and screaming to Robby on the TV. It was good, though. It was difficult, but it was good at the same time, knowing that we won the game. That's what we wanted."
Rivera said that he would continue to shag fly balls in the outfield once he returns to action, saying, "I don't know what the Yankees will do, but they'd better tie me up if they don't want me to."
Rivera added that at no time did he look at last week's injury as a sign that his time in the game was expiring, and that his heart is telling him to continue pitching.
"Only the Lord will take that away from me, if it happens like that," Rivera said. "I don't want to leave the way it happened. If I have to pitch another time that the Lord gives me, I would love to do that. But if I can't, it will be the Lord.
"I will do whatever it takes, but if the leg doesn't come back strong the way I want to, that's the Lord saying He doesn't want me to come back. If it's my call, I don't want to leave the game the way it happened."