The Copa America holders, chasing a third title in as many years, started and finished the contest in the ascendancy but were unable to break down a Germany side who displayed grit and composure beyond their years.
Lars Stindl's winner came heavily against the run of play in the 20th minute, shortly after Alexis Sanchez failed to convert a rebound when Marc-Andre ter Stegen parried a rasping Vidal drive.
Under little pressure, Diaz turned into trouble and allowed Timo Werner to lay on a tap-in for the Borussia Monchengladbach attacker.
"There are mistakes that can happen, but there is nothing to reproach," Vidal told reporters at Krestovsky Stadium. "I think this team is a family and when we win, all of us win."
Vidal bullishly told a pre-match news conference that victory in the final would have established Chile as the best team on the planet.
Falling short of that goal did little to dent the Bayern Munich man's confidence in a close-knit group, with World Cup glory in 12 months' time still the ultimate goal.
"If we won, yes [we are the best team in the world]," he said. "But now, there are many other teams on a great level. We will keep working to be one of the best”.
"I think that our team can leave with our heads held high for the way we have played.
"In every single game, we were looking for the victory. And we played nice football. There is still a lot to come and hopefully we will come next year to fight for the World Cup
"There is nothing to reproach because we fought since the first day. We leave happy to have reached another final and hopefully we keep the same hunger than now.”
Vidal added: "It is an incredible generation. We hope we go through the qualifiers, play the World Cup and reach the final as we did in this cup."
There was a tense moment for Bayern fans during the second half.
As the match threatened to boil over, Vidal and club team-mate Joshua Kimmich were involved in an altercation that saw both men booked.
"I was a bit angry," Vidal explained. "I didn't like what he was doing with his team-mates. They were winning and they were wasting time.
"I was annoyed but we are team-mates and I will see him in 20 days."