[1] Parker is one of five former NFL head coaches (along with Lou Saban, George Seifert, Tom Coughlin, and Mike Shanahan) to win multiple league championships with eligibility to not be inducted into the Pro Football Hall of Fame.

On February 3, 1949, Parker and Phil Handler were named co-head coaches of the Cardinals, replacing Jimmy Conzelman, who had left to work for a local advertising agency.

However, after head coach Bo McMillin found himself in continuous battles with players during the ensuing campaign, he resigned on December 19, with Parker being promoted to the top job the following day.

Parker's superstitions also became legendary, with none of his players ever wearing the number 13, and the team always staying at the Chicago Hilton hotel when playing either the Bears or Cardinals.

However, Parker was not around to enjoy the championship season after stunning the football world by resigning on August 12 during the team's preseason training camp dinner.

In his resignation Parker cited an inability to control his players, but his struggle in obtaining a two-year contract from Lions' management also likely played a role.

During the 1958 preseason, Parker attempted to get the players' attention by cutting five veterans, including Billy Wells, the team's leading rusher the previous season.

The price (quarterback Earl Morrall and two first round draft picks) was steep, but the immediate impact was evident: Pittsburgh improved to 7–4–1, their best record in a decade.

During the latter year, the team challenged despite the retirement of Layne and the tragic off-season death of Eugene "Big Daddy" Lipscomb.

In January 1966, he was under consideration for a Rams' assistant position under George Allen, then was a candidate for head coach of the Washington Redskins in December 1968.

In 1982, he underwent surgery for a ruptured ulcer on March 7 in Kaufman, Texas, but complications left him unconscious until his death fifteen days later.