Silva was also impressed with how City eased back into top gear after the disruption of the recent international fixtures.
The Portugal midfielder said: “Usually after an international break, most teams lose a little bit of the way they play but we were really focused and hungry for more titles and more wins.
“The team has had a fantastic start and are top of the league and in the Champions League we want to beat Shakhtar and go top of the group.
“And we are through in the Carabao Cup, so it’s been a great start. We need to keep it this way.”
City dominated against the Clarets but led only 1-0 at the break thanks to Sergio Aguero’s 149th Premier League strike and it took Silva’s controversial second goal to break the visitors.
City played on after Burnley mistakenly thought referee Jonathan Moss was about to award a penalty for a foul on Leroy Sane by Jack Cork. David Silva remained alert and pulled the ball back for Bernardo Silva to strike, although Burnley complained further as they felt the ball went out of play.
Silva said: “It was a bit strange. At that moment I thought it was a penalty and most of the players stopped.
“But David was smarter, ran for the ball and crossed it. To be honest when I scored I didn’t know if it would be allowed or not but it was a goal and we move on.”
Riyad Mahrez (right) capped a fine performance with City’s fourth goal (Martin Rickett/PA)
Fernandinho added a third moments later and City, who then introduced fit-again Kevin De Bruyne off the bench, coasted to victory with further efforts from Riyad Mahrez and Sane.
Silva said: “Usually against Burnley it’s a complicated game but we were very strong again. The first half was difficult but scoring two early goals in the second half was important.
“But it’s just three points, no more than that, and on to the next one.”
It proved a tough afternoon for former City goalkeeper Joe Hart, who was making his first appearance back at the Etihad Stadium since leaving the club last summer.
It was an unhappy return to the Etihad Stadium for Joe Hart (Martin Rickett/PA)
Hart, who was honoured by City with the naming of a training pitch after him this week, made a number of good saves and did not deserve to concede five.
Clarets boss Sean Dyche, who felt City should have had Vincent Kompany and Leroy Sane sent off for bad challenges, felt the scoreline was harsh.
He said: “Those key moments change the whole game and change the clarity of our performance. That’s learning curve for us but, if you take all that away, was it a 5-0 game? Not really.”
Burnley did at least manage to get 75 minutes out of midfielder Steven Defour, who was making his first league appearance since suffering a knee injury in January.
Dyche said: “That will do him the world of good and we just took him off as a precaution.”
