A rousing comeback saw them pull two goals back in the second half, despite being reduced to nine men when Cesc Fabregas was also dismissed, but it was not enough.
"Instead we conceded three goals and despite a good second half performance it was hard to change the result".
Dyche hinted he was unsure what approach Antonio Conte would deploy in the second half.
Marcos Alonso had an effort saved by Burnley keeper Tom Heaton early in the second half before Alvaro Morata was brought on for Michy Batshuayi, and Alonso had a free kick saved soon afterwards.
Bakayoko was absent through injury against Burnley, along with star man Eden Hazard, while striker Diego Costa has been frozen out after being deemed surplus to requirements.
The Italian also did his best to allay fears about the thinness of his squad. "We're going to work extra hard, even harder than previous year, to make sure we compete".
With the Blues and Liverpool returning to European football, and all top six clubs strengthening considerably in the transfer market along with Everton, Cahill believes the title race will be more open than ever. We had to get on, get the job done and I'm pleased we have done that. In the next game I'm not sure whether Pedro is ready but for sure we'll have (the other) two players.
Chelsea down to 9 men.
"Today big decisions changed the outcome, quite obviously", the Burnley manager said.
"Winning away from home on the first days quietens down some stories - we're written off at the start of every season".
Then it was a case of awful defending that saw the visitors race into a 3-0 lead.
"Our mentality I was really pleased with, to see the game through. And it was weird at half-time because you're three up away at Chelsea and you have to decide how you're going to approach it from there", he added.
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