Shares of industrial and transportation companies fell sharply amid inflation concerns.

While the top-line reading of a 4.2% increase in the consumer price index was softer than economists had anticipated, one brokerage said the report suggested that inflation was becoming more embedded in the U.S. economy.

The report suggested inflation was "sticky under the surface," said economists at brokerage BNP Paribas, in a note to clients, highlighting incipient reversals in the recent retreat of housing and car costs. The BNP economists also said the recent "Beige Book" regional survey from the Federal Reserve suggested that wage inflation is taking hold. "While this is beneficial for workers, it poses a challenge for central bankers who are concerned about the stability of inflation expectations in households' and businesses' negotiations," said the BNP economists.

The danger of the economy overheating is now greater than a stagflationary situation where inflation and joblessness rise in tandem, according to BNP and others. "With inflation projected to run above 4% in our forecast into year end and unemployment to fall to 4.0% by that point, we believe this dynamic will become a more salient risk," said the BNP economists.