NFL Commissioner Roger Goodell believes his job is safe but reiterated that the league could have better responded to penalizing former Baltimore Ravens running back Ray Rice.

When asked Tuesday on CBS if his job at the top of the NFL was on the line, Goodell said, "No, I'm used to criticism, I'm used to that."

"Every day I have to earn my stripes. Every day I have to do a better job and that's my responsibility to the game, to the NFL and to what I see as society," Goodell said.

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The Ravens terminated Rice's contract Monday after video surfaced of a February incident showing Rice punching his then-fiancé in the elevator of an Atlantic City hotel.

The NFL's original two-game suspension of Rice followed video of the player dragging his unconscious fiancé out of the elevator. He was suspended indefinitely Tuesday after the newest video was posted on TMZ.com.

A chorus of critics, including several lawmakers, have questioned the eight-year NFL commissioner for his handling of the case. Some have called for Goodell's ousting and voiced support for former Secretary of State Condoleezza Rice to take over.

Goodell reiterated that the league's initial response to the incident was not "sufficient" but did not rule out whether Ray Rice would be allowed to play in the NFL in the future. 

One incident of domestic violence is too much, Goodell said, adding much of the burden rests on the NFL to do better.

"People expect a lot from the NFL. We accept that. We embrace that. That's our opportunity to make a difference not just in the NFL but in society in general," he said.