There may be a bias issue when former President Barack Obama is praised for using data to enhance his social media strategy and Donald Trump is not, crisis management expert Eric Dezenhall told CNBC on Monday.

Dezenhall, who said he is not a Trump supporter, noted on "Squawk Box" that the public adored Obama after he credited his success during the 2008 election in part by how his campaign used social media.

Now with Trump there is a "whiff of criminality," he said.

"Why is it innovative when the Obama campaign did it and sleazy when the Trump campaign did it?" asked Dezenhall, CEO of crisis communication consulting firm Dezenhall Resources.

"You have an issue of bias here," he added.

An official from Obama's 2008 campaign argued in a weekend tweet against the double standard accusations.

I ran the Obama 2008 data-driven microtargeting team. How dare you! We didn't steal private Facebook profile data from voters under false pretenses. OFA voluntarily solicited opinions of hundreds of thousands of voters. We didn't commit theft to do our groundbreaking work.

The OFA in the tweet refers to the Obama-backed group Organizing for Action.

Dezenhall appeared on CNBC as Facebook shares were down 4 percent in the premarket Monday, after reports Cambridge Analytica, which worked on Facebook ads for Trump, mined the data of over 50 million users of the social network without their permission.

A New York Times report outlined how Cambridge academic Aleksandr Kogan made an app called "thisisyourdigitallife" that prompted users to answer questions for a psychological profile. The news sparked concerns about what personal data is being given to third parties by social media companies.

Facebook said it has suspended Cambridge Analytica from its platform.

Obama's campaign used social media to raise money, organize and successfully fight John McCain in 2008 and Mitt Romney in 2012.

During his campaign, Trump spent millions of dollars on data and digital services in an effort to land donations and win over voters.

Brad Parscale, Trump's campaign's digital director told The Associated Press at the time that "people underestimate our data and digital because we haven't been outspoken about what we're doing."