In treacherous conditions at Rodney Parade, Rynard Landman was sent off during the 30-25 defeat for elbowing Connacht Jack Carty.
The Dragons were up against it throughout and tries from Craig Ronaldson, Mick Kearney and Eoghan Masterson put the Irishmen in a lead which could not be caught.
After being 17-3 down, the Dragons managed to claw back the deficit to only five points with two tries from Hallam Amos and one from Jack Dixon and Jones was proud of the way his players dealt with the red card.
"We are not going to win anything with 14 men on the field," he said. "It was too much for any team, that's why the effort was so pleasing.
"We showed a lot of character, ability and endeavour."
The Welsh club played 65 minutes with 14 men and eventually fell one try short of a bonus point.
Landman's dismissal came in the 14th minute when attempting to charge down fly-half Carty's kick from deep and Jones was highly critical of his captain's conduct.
"It is a kick in the pants for him to understand his responsibility and roles as an overseas player and as a captain while Lee Byrne is out," Jones continued.
"There's no need to raise an arm when charging a kick down."
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