The wording returns nothing in the Library of Congress’s Chronicling America newspaper corpus, nothing in Internet Archive’s text search, and no period book or article. Every carrier that surfaces is a modern quotation aggregator with no citation attached — the classic signature of a line that entered circulation through quote sites rather than through a source.
1938 was also the year of the Jake Powell affair: on 29 July the Yankees outfielder used a racial slur in a live WGN radio interview with Bob Elson, and Commissioner Landis suspended him ten days for “unethical and disparaging remarks.” It is tempting to read Gehrig’s 1938 statement as a reply to his own teammate — but no source consulted here makes that connection, and the sources that mention Gehrig’s 1938 statement give neither its date nor its text.
Two things could still settle this: the text of Powers’s February 1933 Daily News columns, and the wartime pamphlets that quoted Gehrig’s 1938 statement. Neither is freely digitised, and until one of them is read, the honest answer is that the sentiment is Gehrig’s and the sentence is unproven.