Nolan stopped short of urging people to stop driving minicars, but he did say consumers should realize that some slightly larger cars performed very well in front overlap crash tests.
"The Honda Civic is a blueprint for what automakers can do," he said. "It's only slightly larger than the Fit, but it gets the highest score possible in front overlap crash tests."
Honda Fit, Fiat 500 get poor ratings
The safety group said it is most concerned about the performance of two models with "poor" scores: The Honda Fit and Fiat 500.
"In the Fit crash test, there was a lot of intrusion into the passenger cabin. ... And during the Fiat 500 crash test the drivers door was torn open," Nolan said.
(Read more: Consumer Reports likes Toyota Camry again)
In response to the Fit review, Honda issued a statement saying, "Honda has an all-new, completely redesigned 2015 Honda Fit that will come to market in just a few months, and we anticipate it will earn top safety scores from the Insurance Institute for Highway Safety, with a "good" rating in all test modes including the rigorous small overlap front crash test."
Fiat parent Chrysler told CNBC, "The Fiat 500 meets or exceeds all government-mandated safety requirements and continues to offer a high level of protection in four main crash types identified by the IIHS—side, rollover, rear and moderate-overlap front."
—By CNBC's Phil LeBeau. Follow him on Twitter
Questions? Comments? BehindTheWheel@cnbc.com.