Chelsea did try to pull it back in the second half, with two goals.
After being reduced to 10 men in both the FA Cup final and the Community Shield, Conte's men finished the opening game of their Premier League title defence with just nine players after Gary Cahill and Cesc Fabregas were both dismissed in a pulsating 3-2 defeat by Burnley at Stamford Bridge on Saturday.
"We conceded three goals too easily".
Burnley were 3-0 up before half-time, Vokes scoring either side of Stephen Ward's goal, and although Chelsea threatened to claim a share of the spoils, the visitors held on to all three points.
The result will not improve the mood of Chelsea manager Antonio Conte, who hasn't hidden his frustration at failing to significantly bolster his squad in the offseason.
Equally, Fabregas' ban deprives him of another midfielder, with Bakayoko, Hazard and Pedro all out injured. It lasted only 18 minutes, when he was sacrificed as Conte reorganized following Cahill's sending off.
"Instead, we conceded three goals and the second half was very hard to change the final result, despite the great commitment, great desire and great will of my players". "But our first half, we kept losing our heads".
Chelsea have had a turbulent summer, with question marks over the Italian's future until he signed a new contract last month.
Fabregas and Cahill will be suspended for Chelsea's tough second match of the season, away to Tottenham at Wembley Stadium next weekend. "I think by the end you'd have to say we deserved it". "I think that the coach can make mistakes, the players can make mistakes, the referee [too]", he added.
"I repeat: It is important for us to concentrate on our work, to be focused every day in training and to try to work in our best way".
The initial tweet by Burnley underplayed the achievements of Dyche's side, who many felt were relegation candidates given their poor away form last season.