Morata's first goal in the blue of Chelsea came on 68 minutes when he stooped to head home a brilliant cross from Willian and give the Stamford Bridge faithful a bit of hope.
"Chelsea have players of such calibre and to see the game through is so pleasing".
"I am not anxious", Conte said.
Sam Vokes capitalised on the numerical advantage and Chelsea's poor defending, scoring either side of a goal from team mate Stephen Ward, to send Burnley into the halftime break 3-0 up.
Chelsea did try to pull it back in the second half, with two goals.
Alvaro Morata nearly inspired a comeback as a second-half substitute, scoring before setting up a late strike for David Luiz, a goal that came after Cesc Fabregas' removal for a second yellow had seen Chelsea reduced to nine men.
After the opening game of the season on Friday produced seven goals and a late victor for Arsenal, who beat Leicester City 4-3, the two teams at Vicarage Road served up more of the same entertainment for a worldwide television audience - including some poor defending.
It was to get worse for the champions in the first half though as Vokes made it 3-0 to Burnley in the 42nd minute when the striker headed a wonderful Defour cross into the corner of the net. Last year, then-champion Leicester lost at Hull 2-1 in its first match and its fortunes improved only after manager Claudio Ranieri was sacked.
City needed to show patience, with Sergio Aguero breaking the deadlock in the 70th followed by an own goal from Lewis Dunk in the 75th.
"We have to improve a lot on this because after the first red for Cahill we lost our composure and conceded three".
Vokes' second goal came just before the half as he found himself unmarked in the centre of the goal and flashed a header beyond the despairing Courtois.
Sadio Mane, Roberto Firmino, and Mo Salah scored for Liverpool, which was without Coutinho amid interest in the playmaker from Barcelona.
Conte, who named £58million Spain striker Alvaro Mata on the bench, denied a suggestion that his team selection was a message to the board that he is disgruntled over Chelsea's transfer activity this summer.
Huddersfield was English champion three years in a row from 1924.
He left Everton in 2004 as a precocious teenager.