Former IRS Commissioner Doug Shulman isn't overly concerned about this study's findings about tax revenues generated each year.
"There's $3 trillion of taxes that are brought in. The corporate taxes bring in about 10 percent of that," explained Shulman. "Even when a company inverts, they're still paying some U.S. tax on their U.S. operations. They're just out of the U.S. tax net. They're not going to be paying on worldwide operations in the U.S."
Read MoreLew calls for sweeping business tax reform
While President Barack Obama and both parties in Congress agree that the way forward is to lower the corporate tax rate, Bernstein said he believes that tactic can't be the only solution, because the U.S. could never afford to go low enough to beat a country like Ireland, for instance, which boasts a 12.5 percent corporate tax rate.
"We need to do something else to discourage inversions," Bernstein said. "I think the best way to go would be to change the requirement in terms of shareholdings so that instead of the current shareholders continuing to own 80 percent combined value of the new company, it should be moved to 50 percent."
— By CNBC's Marqui Mapp