Pressure appeared to be mounting on Barca, and their head coach Gerardo Martino, after last week's loss to Real Valladolid left them third in La Liga, four points behind leaders Real Madrid.
Barca hit back by seeing off English side City at the Nou Camp on Wednesday to claim a place in the quarter-finals of the Champions League for a seventh successive year.
They will now look to carry that form back into domestic action as they host Osasuna this weekend.
Alves, who scored late in the 2-1 win over City to secure a 4-1 aggregate success, said: "Barcelona always respond like a true great.
"We always want the best version of our team and our play but it can't always come off.
"But we are in the next round, we've played really competitively and when there's adversity, this group of players always responds.
"We may trip up now and again while we are marching forward but we'll stick to the right road.
"We know that nobody remembers the teams who make the knockout rounds - only the champions. That's what we want to be."
Osasuna forward Oriol Riera has also laughed off suggestions that Barcelona are in crisis.
Riera is well aware that his side, who have lost their last two games and are just three points above the bottom three, face a tough encounter.
Riera said: "I would love to be in a crisis if it meant just losing three league games, being in the quarter-finals of the Champions League and the final of the Copa del Rey.
"For me we will be playing against the best possible Barca side and against a great team.
"Playing the top three teams in the league is always very difficult but we go into the game keen to make it difficult for them.
"We will try and stay in the right positions on the pitch so we make sure it's not an easy game for them. At least, that's what we'll try and do."