The holders were beaten on penalties by Paraguay, following hosts and co-favourites Argentina out of a tournament that has been turned on its head by traditional lesser lights of South American football.
Brazil squandered a string of chances before missing four penalties in the decisive shootout to lose it 2-0.
"I'm very firm in my self-criticism [but] Brazil won't get to 2014 tottering, they'll get there strong," Menezes told reporters at his squad's tournament base outside Buenos Aires.
Menezes, appointed last year after predecessor Dunga's failure to get past the World Cup quarter-finals, does not plan to resign.
"I think that to change [coach] doesn't resolve anything. Argentina have been changing quite a lot in the last few years and that didn't resolve Argentina's problem," Menezes said.
His Argentine counterpart Sergio Batista has also pleaded a lack of time to work on his team, although the debate in local media runs much deeper including fears of worse to come after ineffective changes dating back to the Marcelo Bielsa and Nestor Pekerman era that ended at the 2006 World Cup quarter-finals.
Paraguay's Argentine coach Gerardo Martino said Brazil deserved to win. "It had been a long time since I last saw a Brazil team play as well as yesterday."
He also pointed to the bizarre quarter-finals results, saying: "Generally the best team wins but there can be a reverse result [although] it doesn't usually happen as continuously as in this Copa."
LOSING PATTERN
Menezes said that young forwards through whom he is planning to revive Brazil's traditional attacking virtues, like Neymar, Paulo Henrique Ganso and Alexandre Pato, had been fast-tracked into the side due to injuries to more experienced players like Luis Fabiano and Adriano.
"We had to accelerate the process and that, without any doubt, may explain the small hiccups, instabilities as opposed to the consistency we want," he said.
Brazil should have won in the 90 minutes. Paraguay did not have a single shot on target to Brazil's half-dozen and their goalkeeper Justo Villar was the man of the match.
This was a pattern throughout the quarter-finals with Lionel Messi's Argentina creating more than Uruguay and going out on penalties, Colombia coming closer than Peru before losing in extra-time to two shots from outside the box and Chile succumbing to the vastly improved Venezuela.
Chile, regarded by many rival coaches as having played the best football of the tournament, had the chance of a lifetime to end their wait to lift the Copa America after finishing runners-up four times. They were virtually a home side in Mendoza and San Juan just across the Andean border.
They laid siege to Venezuela's goal but could only find an equaliser before a defensive mistake allowed their opponents to snatch a second, late winner.
Their Argentina coach Claudio Borghi said he was unhappy to have lost but said "I don't feel let down, the team played well and we progress
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