The Spaniard was the man to score Chelsea's first Premier League goal of the season with a well-taken header from a Willian cross after 70 minutes, and also assisted a second for the Blues after flicking the ball on to David Luiz.
He added: "We have to think that there is the rest of the game to play and do our best".
Chelsea are unbeaten in the past six meetings with Burnley while the visitors have gone eight league matches without an away win in this fixture.
"We tried until the end to reach a good result against Burnley - it was a pity because our fight in the second half was very good".
"We must focus on working very hard with these players", Conte told BBC Sport after today's game.
After beating Tottenham to the Premier League title last season, the Blues can expect a fired up performance from their London rivals in their temporary Wembley home next Sunday.
After the opening game of the season on Friday produced seven goals and a late winner 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. "In the second half, my players showed great will to try to change the result".
The former Juventus coach nonetheless recognized his team's effort in the second half, with Chelsea in the second period looking much like the team that won the title last season.
It was a nervous time for Burnley fans as Chelsea continued to press.
He has however been a transfer target of big-spending Italian Giants, AC Milan, but it appears their interest has cooled over his insistence to return to the Spanish capital.
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