There are many causes for the Panic of 1873. Rampant inflation in the post Civil War era, a growing trade deficit, massive property damage caused by the Chicago Fire of 1871 and the great fire of Boston in 1872. Economic dislocation caused by the Franco Prussian war and the decision of the new German Empire to stop minting silver coins exacerbated the US trade deficit. There was also a speculative bubble in the stock market, mainly caused by the explosive growth of the railroad industry. The detonator of this growing powder keg was the collapse of Jay Cooke's bank in Philadelphia in September 1873. Cooke was having great difficulty selling the bonds of the Northern Pacific Railroad. He was holding 75 % of the stock of this railroad, but could not raise the cash needed to finish building it. When it went bankrupt, it dragged Jay Cooke's bank down with it and that caused several other bank failures on Wall Street and set off a six year long depression.
Rockefeller did agree to an exclusive contract to ship oil on the Vanderbilt controlled Lake Shore & Michigan Southern Railroad. That was the major east-west railroad through Cleveland OH, where Rockefeller had his major oil refinery. Rockefeller demanded rebates for shipping his oil by train, built oil pipelines to by pass the railroad industry entirely, and by the 1880s, was demanding the Vanderbilt lines pay him a rebate on oil shipped by smaller oil companies. All of this was highly unethical and eventually led to the break-up of Standard Oil, but as early as 1873 Standard Oil was to small and not powerful enough to cause a panic on the scale of the Panic of 1873.
Source: "Historical Guide to North American Railroads" by George Druery