After graduating from Notre Dame, Brennan coached at Mount Carmel High School in Chicago and won three successive city championships.

In 1956, Brennan had mostly sophomore starters, due to numerous injuries; the result was a 2–8 record, and the first losing season for Notre Dame since 1933 and the worst in school history.

Among their victories was a 23–21 comeback over Army and a 7–0 shutout of Oklahoma, snapping the Sooners' NCAA record 47-game winning streak.

After a 6–4 record in 1958, the movement to dismiss Brennan gained momentum, and the coach was fired along with his entire staff in mid-December; Hugh Devore was eventually retained.

Brennan served as player conditioning coach for baseball's Cincinnati Reds during spring training in 1959 and eventually joined a Chicago investment banking firm.