England's points came from four Olly Barkley penalties and an Andy Gomarsall dropped goal but they might have had several tries with more clinical finishing.
"It is very disappointing," Catt told Sky Sports. "The commitment was there and we showed a lot of heart but our execution let us down.
"It was an established and experienced French side and they closed us down pretty well but we seemed to be a bit rusty as a team and we have got to iron out the mistakes."
But Catt believes that despite today's setback England are making general progress and added: "We've come a long way over the last eight weeks and that has put us in good stead to move forwards."
A delighted Chabal said: "It was a good win for us. Everything wasn't perfect - we lost a few lineouts in the first half - but next week we will try to pick our best side."