Romney spokesman Eric Fehrnstrom was asked by CNN anchor Erin Burnett whether concern over his sexuality prompted Grenell's exit from the campaign.
"Obviously it sounds there, reading between the lines, that the focus on his personal decisions, on perhaps his sexuality, was why he chose to go. Maybe not because it was happening in your campaign, but it was happening by others in the Republican Party?" Burnett asked.
"Yeah, and that’s disappointing. Wherever there are voices of intolerance within the party, or the Democratic Party, for that matter, it doesn’t matter where it’s coming from, it’s disappointing. And the governor has taken the opportunity in the past to denounce those voices of intolerance," Fehrnstrom replied.
"We do not take into consideration non-factors like race or ethnicity or sexual orientation. We look for the best possible people to do the job," he added.
The Romney campaign said in a statement earlier this week that it had asked Grenell to stick with the campaign.
"We are disappointed that Ric decided to resign from the campaign for his own personal reasons," Romney campaign manager Matt Rhoades said. "We wanted him to stay because he had superior qualifications for the position he was hired to fill."
Fehrnstrom also emphasized that Romney's campaign tried to talk Grenell out of leaving when the issue was first raised.
The Obama campaign has already criticized Republicans for Grenell's resignation.
"Today we learned that in the year 2012, a Republican nominee for president can't have a gay person as spokesman," Obama for America Digital Director Teddy Goff tweeted Tuesday.