Ha, that is the exact moment my hatred for the Jets began!
The Patriots had a very good team in the sixties, but first the Oilers, and then the Bills were always just a bit better. In those days there were no playoffs in either the AFL or the NFL; just two first-place teams playing for the championship. A second place finish meant no post-season.
The 1966 season turned out to be the last hurrah for that group, though I never would have guessed it at the time. Parilli was 36 and it was about a decade before the Patriots got another decent QB. After a slow start (in part due to consecutive road games, as they couldn't play at Fenway yet) the Pats went 7-1-1 over the next nine games. The tie was at Kansas City and it looked as though there would be a rematch with the Chiefs for the AFL championship - and a chance to represent the league in the first-ever game against the NFL champions. This was a really big deal for kids my age, even if it was not so for those of my parents' generation.
All that was needed was a win against the five-win Jets, who had not beaten a team with a winning record all season. The Pats were coming off a 38-14 victory over Houston, and would surely avenge an early season tie against the Jets. Namath was in his second season as a pro and still looked raw and inconsistent, but he threw three touchdowns while Matt Snell and Emerson Boozer both ran for over 100 yards. The Patriots turned the ball over three times while not forcing any turnovers and lost, 38-28.
Perhaps they were looking ahead to KC - I truly believe the Patriots would have beaten the Chiefs. It was ten years before the Patriots would have another winning season - and another heartache - when they lost to Oakland in the Ben Dreith game. Meanwhile the Jets went on to win the Super Bowl the following year.
On top of that, at that point in time the Patriots and Red Sox were in talks with the state and city to build a new stadium at South Station, plus a new arena there for the Celtics. Tom Yawkey wanted badly to get out of Fenway, which was a craphole at that time - and the Celtics wanted to get out of being second-fiddle tenants to the Bruins in an ancient Boston Garden. The next year though the Red Sox had their Impossible Dream season, and attendance went from under 10k per game to 30k. Yawkey saw no reason to move the team with that extra cash rolling in, and the Patriots hunt for a stadium continued. Without the Sox and Pats working the politicians together for a new venue, that new stadium in the city never happened.
Apologies for the long ramble, but yeah - I hate the Jets. The Jets still suck, and will always suck.