Khan, 43, one of India's best known actors, was en route to Chicago for a parade to mark the Indian Independence Day when he was pulled aside and questioned at Newark airport on Friday.
"I respect that my name pops up on the computer and I also agree that I don’t need to be treated specially, I am nobody," Khan told a news conference at his residence a few hours after returning to Mumbai.
"They asked me some questions which I thought was a little embarrassing. But if a procedure has to be followed, it should be done properly," he said.
Khan's detention caused uproar among fans in India. Newspapers and TV channels termed it an instance of racial profiling and the controversy sparked debate in the media.
"I was really hassled, perhaps because of my name being Khan. These guys just wouldn't let me through," the actor had said in a text message to reporters on Saturday.
On Tuesday, Khan sought to play down the controversy and said he wanted to "move on".
When asked if he would go back to the United States, the actor said he would cut back on trips to the country.
"It is not a matter of pride for me that I was questioned at the airport," the actor told reporters.
"I don't want to sound pompous but Shah Rukh Khan doesn't need publicity stunts to be in the public eye."