The Italian was especially pleased with new boy Alvaro Morata, who came on with the team three goals down and scored one.
Chelsea were reduced to nine players in the 81st minute when Cesc Fabregas was shown a second yellow card but Dyche felt his team deserved the win.
"Chelsea have players of such calibre and to see the game through is so pleasing". Good service from the flanks is imperative and Perisic scores highly in that department despite playing in a lacklustre Internazionale side.
"We kept going, kept probing and it's 3-0 at the interval".
"It's a great win for us, brilliant for our players, brilliant for our supporters but we know there's a big season right in front of us, the "second season" that everyone's telling us about".More news: Trump orders probe of China's intellectual property rules
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Chelsea's manager Antonio Conte, left, watches the match during the English Premier League soccer match between Chelsea and Burnley at Stamford Bridge stadium in London, Saturday, Aug. 12, 2017.
The visitors were the better side overall with a disciplined, energetic and ruthless first-half display that saw them put three past the Blues, with Sam Vokes netting twice.
"I repeat: it is important for us to be concentrated on our work, to be focused every day in training and to try to work in our best way".
Last season, Burnley failed to record an away victory in the league until late April, relying heavily on their Turf Moor form to stay above the relegation zone.
"We keep moving it forward, now can we move it forward again?"
As well as defender Terry and midfielder Matic, Chelsea have sold Asmir Begovic to Bournemouth, while last season's top scorer Diego Costa has been told he is free to leave. It's very hard for this club to make massive strides, so it's about just shifting it forward.