With just four games remaining in the season, the Islanders are bottom of La Liga and four points from safety, a situation which Manzano admitted obliges them to go for the win against Marcelo Bielsa's side.
He told a press conference: "They opt for a bold and adventurous way of playing and we have to exploit that by doing a good job in midfield, making the most of our chances and doing our defensive duties correctly. We need to get things right at both ends.
"We have to travel with the exclusive aim of going there to win and try to do that in a beautiful stadium, with a great tradition of football and against a team that are also playing to avoid relegation.
"In effect, it's a crunch match which needs to be played by real men."
Mallorca missed a huge opportunity to move off the bottom of the league last weekend by failing to beat Levante at home, but Manzano has refused to give up hope of remaining in the top flight.
He pointed out that the club avoided the drop in 2004-05 despite being in the same position they are now in at this stage of the season, adding the game at San Mames was "a new opportunity".
"The only battle lost is the one that is abandoned," he added.
"We will gain nothing from pessimism or negativity. We have a new opportunity in Bilbao and we have to grab it with both hands."
Athletic may be nine points above Mallorca in the table but they have still not sealed their status in La Liga for next season, leading Bielsa to say the match was of equal importance to the Basques.
"For them it's a must-game win, just like it is for us. Winning for us is just as indispensable to us as it is to Mallorca," he insisted.
The Argentinean is confident his team will avoid the drop and believes they deserve to because they have continued to play attractive football despite their desperate situation.
"We have never stopped fighting and our struggle has been serious, responsible and correct," he stressed.
"We have played quality football and used noble weapons. In fact, we have stuck together and we respect each other, despite the fact that in adversity it is normally difficult to stay united."
Ander Herrera will return to the Athletic side after missing the 1-1 draw with Celta Vigo due to suspension and Bielsa explained that he would drop Ander Iturraspe to the bench to make way for the former Zaragoza player, while Ibai Gomez would return to the starting line-up.