Juve won a fourth consecutive scudetto last season and secured their first league and Cup double in 20 years before ending a 12-year wait to challenge for the Champions League final last May.
But after defeat to Udinese last week, a depleted Juve succumbed 2-1 to scudetto rivals Roma after a lively encounter at the Stadio Olimpico on Sunday.
Juventus, who underwent significant changes in personnel during the summer following the departure of Andrea Pirlo, Arturo Vidal and Carlos Tevez, now sit 17th in Italy's top flight after two games.
Buffon admitted the club's new players will need time to find their feet, but with holes in the defence and yet another lacklustre performance coming from French midfielder Paul Pogba, the legendary Italy goalkeeper said the champions ultimately failed to show up.
"When you play for Juventus, winning is everything, but even when that doesn't happen you need to offer more than we showed today," Buffon said after the game.
"When the team undergoes a lot of changes of course you can allow for a few dropped points or for some nerves to creep in at the start.
"But we have lots of new and quality players, so everyone should be taking on a greater sense of responsibility, starting from when we regroup next Monday."
Second-half goals from Miralem Pjanic and Edin Dzeko, who nodded home in the 79th minute, left Juventus with a mountain to climb at the Stadio Olimpico.
Juve wing-back Patrice Evra had been sent off for a second bookable offence in the latter stages and although Juve grabbed a consolation through Paulo Dybala, the champions had little in response to a well-oiled Roma side that seemed destined for the win.
It was Roma's first league win over Juve since February 2013 and meant the Italian champions have failed to win their first two league games of the season for the first time in history.
For Buffon, Juve's "deficiencies" meant the champions weren't even worthy of the draw.
"We wouldn't have deserved the draw. We had a lot of deficiencies, especially in midfield, but that's no excuse," added the goalkeeper.
"They played better than us and came right at us. We were too timid and lost confidence when things started to go wrong."
From the highs of the Champions League final, where Juve suffered a 3-1 defeat to Barcelona, the Turin giants have plummeted to the lower reaches of Italy's top flight to sit fourth from bottom ahead of Empoli, Frosinone and Carpi.
The Serie A campaign, however, is only two weeks old and coach Massimiliano Allegri is confident normal service will resume following the break for international football next week.
By that time, German international midfielder Sami Khedira, who has yet to make his league debut, and Italian counterpart Claudio Marchisio are expected to be fit to play.
Spain striker Alvaro Morata, who linked up well with Tevez last season, should also be fully fit having recently returned from a knock.
"We've some catching up to do, but we have the time and the quality to do so. We have to stay calm, clear-headed and analyze what didn't work for us," said Allegri.
"When we come back we'll have Marchisio ready and Khedira won't be far off. Morata will be in better shape, while (Juan) Cuadrado, Mandzukic and Dybala will be more in tune with our our way of working."