England had put pressure on the visitors in second half with only Andy Gomarsall's drop-goal as a reward, and Ashton feels his players will have little chance of defending their World Cup next month in France without showing a killer instinct to finish teams off.
"You play in a game like that and work incredibly hard to put yourself into a position to win it by opening up three or four opportunities in the second half and you blow every one of them," he said.
"You don't win big games against good sides playing like that. You don't win World Cups playing like that, either.
"It was a very angry dressing room, I hope the messages of today will be taken on board very quickly and not repeated next week."
Ashton's men face France in Marseille next week - this defeat was their last warm-up at home - and he has hinted at playing his strongest team.
Before that encounter, Ashton will select his squad for the World Cup and he admits the defeat has changed his mind on some of his players, a day after he stated that most of his selection work had been done.
Olly Barkley had given them an early lead with a penalty before Fabien Pelous, earning his 111th cap to equal the French record, went over in the corner.
Barkley's boot gave England a half-time lead which was extended by Gomarsall but Chabal came off the bench to devastating effect, scoring his try with nine minutes remaining.
Not even Jonny Wilkinson coming off the bench in the dying moments could prevent defeat. It meant England missed out on five successive home wins under Ashton, following their win over Wales last week.
"I thought we competed in most areas of the game against what was a very strong French side, pretty close to their strongest selection," added Ashton.
"We made a substantial number of changes last week and there was the fear going into the game that it might mitigate against us but I don't think it did.
"We defended very well, it was tougher this week and the forwards battled well. It was just the second-half execution when we got in their final 22, it let us down."
Ashton will also make an assessment of a possible thigh injury to Mike Catt.
In contrast to Ashton, France coach Bernard Laporte was delighted with the efforts of his team.
"We did what we had to do - to find the solution to the game," he said.
"It's what we said before, that the game the score wasn't important, it was the way we played after we've been training for six weeks
"It's more the way they played today that we are happy about and the solidarity they showed.
"One of the good points of the afternoon was the defence, we controlled the game."