Goals from Stephan Lichtsteiner, Sebastian Giovinco and Paul Pogba ensured what turned out to be a comfortable victory for the hosts, who extend their lead at the top of Serie A to seven points.
However, Conte was left disappointed, despite the victory, as the Bianconeri faithful resorted to jeering the players, particularly goalscorer Giovinco, before they eventually took control of the game.
“Unfortunately booing is becoming a bad habit at this stadium, supporters can’t boo the lads’ first mistake," he told the official club website.
“I’ll remind them that this team has done extraordinary things, but above all brought back a sense of belonging and pride to all Bianconeri fans.”
He told Rai Sport: “At times certain murmurs of complaint from the stands really irritate me, as I find them inopportune. People forget that 18 months ago Juve were seventh.
“They ought to be enthusiastic at having players like Giovinco, so I do not agree with those who jeer.”
Conte was pleased, however, with the way his side handled a potentially tricky encounter as Beppe Iachini's men had gone three games unbeaten before Sunday's clash.
He continued to the official club website: “We took to the field with a good approach, showing great respect for Siena who possess all the characteristics required to stay up.
“They’re in good form and came into the fixture following important results. I knew it wouldn’t be easy and that’s why I kept the tension high.
“Congratulations to the lads, they really did well today. I’m happy about Giovinco’s goal and for how it came about. We always look to work on every little detail, including set pieces.”