The Blues managed to score a second in the 88th minute when David Luiz converted a flick from Morata, but Burnley, who hit the post late on through Brady, held on to record all three points following an incredible game at Stamford Bridge.
He did insist, though, that he was still fully focused on defending the club's Premier League title this season irrespective of any other concerns.
"Before that, we´d kept a good shape and I don't think they opened us up or made too many chances".
The champions slumped to a 3-2 opening day defeat against unfancied Burnley, shipping three goals in the first half after Cahill was sent off for a risky tackle.
There was no such nonsense from Antonio Conte, but he must be regretting his comment last month when he said "wants to avoid a Mourinho season", referring to the 2015 meltdown.
"It was a pity because our fight in the second half was very good", said Chelsea manager Antonio Conte. In the next game I don't know if Pedro is able to recover from his injury, but for sure we will have two players out for a ban, Cahill and Fabregas.
Replacing Michy Batshuayi with almost an hour gone, Morata entered the game with his team 3-0 down after a nightmarish first half.
Burnley doubled its lead after 39 minutes, Ward playing a one-two with Jack Cork before unleashing an excellent half volley into the far corner.
Big-spending Manchester City won 2-0 at promoted Brighton and Hove Albion, while Huddersfield Town marked their top-flight return with a 3-0 win at Crystal Palace that sent them top of the table.
"Did we expect this situation?"
Morata's start to life as a Chelsea player has not had the ideal start, missing a penalty in the Community Shield defeat to Arsenal on Sunday. A quick free-kick led to Defour swinging in a cross from the right and an unmarked Vokes planted a header past Courtois, with loud boos greeting the champion when the half-time whistle was blown.
Ahmed Hegazi scored in his debut for West Brom, on loan from Egypt's Al Ahly.