The Federal Reserve was worried that inflation may become so entrenched in the U.S. economy that the public would question its resolve to fight it, minutes of its June policy meeting revealed Wednesday, as it unveiled the biggest hike in three decades and argued for more "restrictive" rates over the coming months.

The minutes indicated that a larger-than-expected rate hike was needed in June in order to tame the fastest inflation in four decades, noting that the outlook for consumer price increases had deteriorated leading up to the June 15 decision.

The Fed lifted its base lending rate by 75 basis points, the biggest since 1994, to a range of 1.5% to 1.75% last month and said near-term rate moves would be needed in order to combat the fastest inflation since the early 1980s. The Fed also raised its forecasts for U.S. unemployment, to a rate of 3.7% from a prior forecast of 3.5%, while cutting its 2022 GDP growth estimate to 1.7%, well shy of its previous indication of 2.8%.

"Elevated inflation could become entrenched if the public began to question the resolve" of the Fed to fight it, minutes from the central bank's June meeting revealed.