Ten minutes into the Twickenham game, a melee broke out when Wales had a try disallowed for a George North knock-on and the incident involving Marler and Jones was caught on camera.
"You can be a great player, a character and different but don't go around being a distraction and embarrassment to the team, shirt and country," Woodward, who coached England to World Cup glory in 2003, wrote in his for the Daily Mail.
"I knew England were in big trouble before the World Cup final (last year) when Joe Marler started horsing around at a bizarre press conference with Dan Cole. That was embarrassing, disrespectful and said much about the team's mindset.
I wouldn't stand for that and... nor should the team. We saw it again with his ridiculous groping at Jones' genitalia... perhaps he thinks that's clever... but it'll be interesting to see how the Rugby Football Union handle this. I know what I'd do.
Prop Marler, 29, is likely to be cited by the sport's governing body World Rugby.
According to its law 9.27, "a player must not do anything that is against the spirit of good sportsmanship" with grabbing, twisting or squeezing the genitals warranting a minimum suspension of 12 weeks and a maximum of four years.
England's victory took them to 13 points from four games, level with France. Their final game against Italy in Rome was postponed due to the coronavirus outbreak. (Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Michael Perry)