Norwich responded after the break and, when Ba scuffed his shot in front of an empty net, the hosts were level through Anthony Pilkington, who earlier might have earned a penalty after being tripped by Ramires.
However Norwich saw all of their hard work undone in the final five minutes when a poor back header was seized on by Eden Hazard, who squeezed the ball under England goalkeeper John Ruddy, before Willian cracked in a superb angled drive to clinch a 3-1 victory for Chelsea.
Hughton said: "I generally felt, on the balance of play after conceding a poor goal so early and giving them that momentum, we couldn't have asked for any more effort and determination.
"It was their second goal which hurt us. It came from our corner and we were set up very well, but their power and pace on the counter-attack got the better of us, then at 2-1 it became very difficult for us.
"You have to hold your hand up sometimes: the strike for the third goal, they have that kind of quality."
Hughton felt his side should have been given a spot-kick when Pilkington was tripped by Ramires.
"Anthony gets to the ball first, and with Ramires' action, then he ends up going over. Generally that is a penalty, but it is disappointment.
"Still, the players put in a really good effort. Our supporters appreciated what they did and I felt we deserved to get more."