- In his latest statement, United CEO Oscar Munoz said the airline took "full responsibility."
- Munoz's apology came a day after video of Dr. David Dao of Kentucky being dragged off an overbooked flight went viral.
- The stock ultimately closed down just over 1 percent.
Somebody made a big mistake by dragging a passenger from a United flight, but the airline's CEO did "exactly the right thing" by apologizing on Tuesday, former American Airlines CEO Bob Crandall told CNBC.
In his latest statement, United CEO Oscar Munoz said the airline took "full responsibility" and vowed that a thorough review would take place.
"Like you, I continue to be disturbed by what happened on this flight and I deeply apologize to the customer forcibly removed and to all the customers aboard. No one should ever be mistreated this way," Munoz said in a statement.
"That's what he should have said yesterday. He knows that now," Crandall said in an interview with "Closing Bell" on Tuesday.
Munoz's apology came a day after video of Dr. David Dao of Kentucky being dragged off an overbooked flight went viral on social media. The confrontation happened on a United Express flight operated by Republic Airways.
The CEO at first apologized for having to "re-accommodate" customers after a two-hour delay. He also sent a letter to employees Monday evening that claimed employees "followed established procedures" when removing the passenger from the plane.
Shares of United dropped on Tuesday and were among the worst performers in the . The stock ultimately closed down just over 1 percent.
"Somebody made a big-time mistake. They shouldn't have done it and they know they shouldn't have done it," Crandall said. "I'm sure it's taught everybody a useful lesson and hopefully everybody can now move on."
The incident has shone a light on the practice by airlines to overbook flights, causing people to be bumped. However, Crandall pointed out that "a very, very big majority" give up their seats voluntarily.
And he believes industry will continue to try to find ways to entice people to do so.
"The way you get people off is you raise the price to get people to voluntarily give up their seats. You don't get on and drag somebody off, and I think everyone in the Western world now knows that," Crandall said.
Meanwhile, former pilot Denny Kelly believes it was the passenger who made the error.
"The folks at United did what they were supposed to do. Just because you buy a ticket doesn't guarantee you that you're going to get to travel," he told "Closing Bell."
"The guy made a big mistake in refusing to get off the airplane. The other three people … got off with no problem."
What's more, he doesn't think the industry is going to change its procedures when it comes to bumping people off of flights.
"The airlines' got too much power. Nothing's going to change. It's going to be the same way. The airlines are only interested in one thing and it's the bottom-line profit. This will go away maybe tomorrow, maybe a week from tomorrow but it will go away," said Kelly, who is now an aviation consultant.
— CNBC's Fred Imbert and Matt Rosoff contributed to this report.