Before the game Conte had been at pains to stress the psychological importance of resisting an in-form Siena team with a Serie A title clash against Napoli and Celtic's second-leg visit to Turin approaching fast.
But at the final whistle Juve had made light work of Giuseppe Iachini's side, with goals from Sebastian Giovinco and Paul Pogba completing a 3-0 win after Stephan Lichtsteiner bundled home the opener.
Conte told juventus.com: "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. 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."
With the season entering its crunch stage, Conte urged the home faithful to get fully behind his team.
"Unfortunately booing is becoming a bad habit at this stadium, supporters can't boo the lads' first mistake," he added.
"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.
"My lads deserve respect, they're all committed to following me. They all know that we mustn't lose sight of our target and can only reach it through endeavour and sacrifice.
"Hard work is the reason behind us commanding top spot for a year and our proximity to the Champions League quarter-finals."
There was further good news for Juve as medical tests confirmed defender and vice-captain Giorgio Chiellini had merely sustained bruising to his right ankle during the game.
Relegation-threatened Siena were never likely to claim all three points at the Juventus Stadium but Iachini was disappointed his players let the oppression feel of a sold-out stadium affect their game.
"In the beginning we suffered because of the environment at Juventus," he told acsiena.it. "Then we wrestled back a bit of control on the pitch but unfortunately we could not get back into the game.
"They were more cynical than us and they took advantage of that fact whenever they could. The end result was a little unfair, even if Juve are a great team and very difficult to deal with.
"Nothing changes for us and we must continue on the path towards securing our survival."