Some NFL players criticized Cutler, who stood watching the game in a heavy coat while the Bears fell to a 21-14 loss to the Green Bay Packers, through disparaging comments made on social media sites.
Jacksonville running back Maurice Jones-Drew posted on his Twitter account: "When the going gets tough........QUIT." He followed that with: "All I'm saying is that he can finish the game on a hurt knee ... I played the whole season on one."
But the Bears later said that Cutler, who injured his left knee in the first half of Sunday's game but only left for good after the first series of the third quarter, suffered a medial collateral ligament (MCL) injury to his knee.
"I haven't seen it before," Smith said at a news conference on Monday. "It seems like if you're in that fraternity you would be stepping up for your fellow man, especially when you don't know.
"Jay didn't take himself out of the game. He wanted to go back in. He was injured and went back in the second half. So I see it as the complete opposite of how it's being portrayed right now."
The issue of Cutler's injury and whether he should have played through it dominated sports radio shows on Monday along with the Twitter snipes from players on other NFL teams.
The Bears said Cutler received treatment at halftime before reentering the game in the third quarter. He threw an incomplete pass in a three-and-out opening drive to start the second half before leaving the game for good.
"Our quarterback's a tough guy. He wanted to win the game as much as anyone. It's pretty simple what happened yesterday. Before the half, Jay hurt his knee. He showed a lot of toughness to continue to play with it. The medical staff, we all made the decision then that he couldn't go."
(Reporting by Simon Evans in Miami; Editing by Frank Pingue)