Everton suffered a 3-0 defeat to the French giants, despite keeping them at bay until the hour mark before Bertrand Traore raced through to latch onto a loose ball and round goalkeeper Jordan Pickford.
Houssem Aouar put Lyon two goals to the good with an exquisite finish from the edge of the area that nestled into the bottom corner, before Schneiderlin needlessly dived in to earn a second yellow card.
Memphis Depay scored late on, leaving Everton with just one point from four Europa League matches and now with no chance of qualifying for the last 32 after Christmas.
Jenas told BT Sport, as quoted by their official Twitter account, that 27-year-old Schneiderlin's sending off was "borderline disgraceful" before commending Everton for a brave effort until everything "fell apart".
"It's a shame though," Jenas said. "In the second half I thought they came out with more energy, they looked like they were trying to score and getting players closer to Gylfi Sigurdsson.
"Then it just completely fell apart. A total capitulation, I think the Schneiderlin sending off is borderline disgraceful and unprofessional and he's not given his teammates any help.
The defeat leaves Everton boss David Unsworth with three losses from three matches, after being knocked out of the Carabao Cup by Chelsea and losing to Leicester in the Premier League.
It remains to be seen if the Toffees hierarchy will bring in a new manager before Sunday's match against Watford at Goodison Park, which many pundits have described as must-win.