"At that time nobody knew what the evolution of the Super Bowl would be like," said Stram, who was in town to speak at a fund-raiser for Bishop Museum.
After all, the game wasn't even known as the Super Bowl then. The super tag was added later by NFL commissioner Pete Rozelle. Initially, the game was simply known as the AFL-NFL World Championship Game.
The NFL's Green Bay Packers defeated Stram's Kansas City Chiefs, the AFL champions, 35-10, in the inaugural event at the Los Angeles Memorial Coliseum.
Everyone remembers the Packers and Coach Vince Lombardi. Super Bowl losers aren't always remembered, unless they go 0-4 like the Minnesota Vikings, the Denver Broncos and the Buffalo Bills.
The Chiefs might have been the first Super Bowl loser, but they won it three years later under Stram, beating the Vikings. Stram remains as the all-time Kansas City leader in coaching victories (124).
Stram coached the Chiefs even before they became the Chiefs. He and owner Lamar Hunt started with the Dallas Texans of the old American Football League.
"One of us had to leave town," said Stram, referring to the NFL rival Dallas Cowboys. He thought it was going to be the Cowboys. They were losing and the Texans were winning. However, Hunt moved the team to Kansas City in 1963.
"Shows you how dumb I was, I wanted to keep the name Texans and Lamar agreed with me," Stram said. "I guess that didn't go over big with the people in Kansas City."
"IT was a glorious time in the history of the Kansas City franchise," said Stram about his years with the Chiefs. And who can ever forget the dapper Stram on the sidelines, exhorting his team with a rolled-up wad of paper.
"People always asked me what it was," Stram said. "I just tell them it's a quarterback guide and a grocery list for Phyllis (his wife).
But Stram, 73, who'll be doing an NFL show for CBS radio this fall, could give you a personal list of his all-time great football players who made his job easier - Buck Buchanan, Willie Lanier, Jan Stenerud, Bobby Bell and Len Dawson, who are all Pro Football Hall of Famers.
Stram's ability in finding that certain special quality in a player paid off in Dawson's case. Drafted No. 1 by Pittsburgh and later sitting on the Cleveland Browns bench for five years, Dawson threw only 44 balls during his first six years as a pro.
But Stram knew Dawson from Purdue, where Stram was an assistant coach for eight years and doubled as the varsity baseball coach.
So he persuaded Cleveland's Paul Brown and made a deal for Dawson. Brown agreed with a caveat: "I don't want you to say I gave you damaged goods."
"Well, the rest is history, as they say," Stram said. "Lenny was the AFL player of the year in his first year in 1962."
THAT'S how Stram also remembers a big tight end from Hawaii named Jim Nicholson, now a local attorney, who played for Stram and the Chiefs.
"When I was at Miami, we played Michigan State and one of the players Duffy Daugherty talked at great length about was Jim Nicholson," Stram recalled.
So he made it a point of acquiring Nicholson in a trade with the Los Angeles Rams. "He was a very fine offensive lineman, big and tough. He had a personality of a defensive player playing offense."
Actually, Stram's Hawaii ties go back even further - to the 1950s - during his Purdue days. "We had players like Bino Neves, Johnny Kerr, John Simerson and Al Espinda from the islands. We never had a bad kid from Hawaii."