Conte's men secured back-to-back Scudetto titles last weekend but missed out on beating the record 91 points tally from the 2005/06 season, when they were stripped of their Serie A title for match-fixing, as they were held by Cagliari on Saturday.
 
Juve needed two wins from their final two matches of the season to surpass the points record, but were held to a 1-1 stalemate to leave them with 87 points heading into the season's final day next week.
 
Conte said the toughest challenge for his side will be emulating their dominance of Italian football in the 2013/14 season, when they will be hunting a hat-trick of top-flight titles.
 
"Thinking of the future, it is surely the most difficult aspect to face for us now, after the two last extraordinary seasons that we have won two Scudettos and becoming the leading club in Italy, as we were in the past," he said.
 
"It's definitely great (being champions), it's a great honour but also a great responsibility, and next season will be much tougher for us, both to reconfirm our value in Italy and also to be among the first eight teams in the Champions League.
 
"We need to be good and understand we will have more work to do, we will need more sacrifice and determination, enthusiasm and stamina to go ahead.
 
"If we bear in mind this, we will have a good chance to do something important again, otherwise it will be tough for us next season."
 
Conte said he was not as concerned about his players' physical welfare as he was their mental capacity to embark on a third straight Serie A title – a feat the Torino club has not achieved since winning five straight championships from 1930-35.
 
"Before working on the physical and tactical aspect you need to work on the psychological side," he said.

"If you don't have your mind focused, legs don't run; there are the essential elements for me: mind, heart and legs, and in this order, because mind leads everything and then a player should always have a great heart."
 
The stalemate with Cagliari at Juventus Stadium did not dampen spirits among the faithful, who Conte commended for their support.
 
"Our supporters were great, they were extraordinary. They deserved this, and they always deserve the best," he said.