Griffin only left Sunday's 24-14 loss to the Seahawks when he injured himself while trying to grab a bad shotgun snap in the fourth quarter, but critics are suggesting the face of the Redskins should have been taken out of the game earlier.
"Robert is our franchise quarterback. I am not going to take a chance on his career to win a game," Shanahan said.
"But I also know that when you have got the belief in the guy and you feel that he can play at a certain level and the doctor is telling you that he is OK to go in - then you have got to do what you think is right.
"If I didn't think he was right then he wouldn't have been in, its just that simple," added Shanahan, who said he spoke to team doctors on the sidelines on four occasions during the game.
Griffin, who led the Redskins to their first NFC East title since 1999, will head to Florida on Tuesday to see Dr James Andrews and have further tests after an MRI proved inconclusive.
Speaking after Sunday's loss, Griffin said he clearly told the coach he was able to play but conceded he had put himself at risk by playing with the injury.
"I think I did put myself at more risk by being out there but every time you step on the field, you're putting your life, your career and every single ligament in your body in jeopardy," said Griffin.
The Redskins had led the wild-card play-off game 14-0 in the first quarter but Griffin struggled through the rest of the game until walking off the field under his own power.
Shanahan said he was well used to criticism but it was clear he was stung by some of the commentary in the hours following the Redskins' home loss.
"As a head football coach, used to criticism, you make decisions based on what you think is the right thing to do. You listen to a lot of different people, you get their opinions," said Shanahan.
"Then you make the call and you have to do what you think is right. If people got a chance to be in your shoes, to be around the scenario then maybe they would understand the decisions you make.
"To think we are going to question (risk) a guy's career to win a game is crazy."
Shanahan said he had no indication about the seriousness of Griffin's knee injury but said the need for new scans was based on clarifying whether he had a recurrence of previous anterior and lateral ligament injuries.
"Anytime you have a former ACL or LLC and you take a look at the MRI, sometimes it is old injuries, that is why he is going to fly down to see Dr Andrews and get some new MRIs get a physical examination.
"Right now, everything is total speculation," he said.
Andrews caused controversy on Sunday when he contradicted Shanahan by saying he had not authorized Griffin's return to the game after being injured in an earlier game - the December 9 regular season win against the Baltimore Ravens.
Shanahan repeated his stance that Griffin had been given clearance by Andrews and when asked if the doctor's comment put him in a bad spot he said "Sure does, sure does."
