He played in seven AFL Championship Games, the only man to do so; with the Chargers in 1960 and 1961, 1963, 1964 and 1965; and the Oakland Raiders in 1967 and 1968, winning one with each team.

He was selected second-team tight end on the American Football League All-Time Team.

Kocourek participated in nine playoff games in a span of seven seasons, catching 15 passes for 257 yards and 2 touchdowns.

Kocourek served as a color commentator on NBC's AFL and NFL telecasts in the late 1960s and early 1970s, and teamed up with Mark Champion to broadcast Tampa Bay Buccaneers games on the radio in the late 1970s and early 1980s.

Kocourek died on April 24, 2013, in Marco Island, Florida after suffering from progressive dementia.