What causes inflation is having too much money chasing too few goods. (We’ve had periods of inflation and deflation before the Fed existed, and we’ve had periods of deflation and inflation after it existed.) The Fed, however, is a way of managing our money supply to limit the preponderance of financial disasters.
To say that the tool (Fed) causes an outcome (inflation) is like saying that guns shoot people. ;)
By the way, without the Fed, we had similar banking crises in 1814, 1818, 1825, 1836, 1841, 1857, 1861, 1864, 1873, 1884, 1890 and 1907, or an average of one every 8 years. (The Bank of England bailed us out in 1836 and 1857, and J.P. Morgan in 1907.) I tend to favor the banking system that had banking crises in 1914, 1929, 1984, and 2008, or an average of one every 25 years.