The Rossoblu head into the international break without a win to their name and lying 19th in the Serie A standings with just three points from seven games.
Sunday's 4-1 home defeat to Hellas Verona followed their 5-0 reverse at Roma and marked their fourth loss of the campaign.
"We only have ourselves to blame and we must get our hands dirty and continue to work in order to recover the ground we have lost," Zanzi said on the club's official website, www.bolognafc.it.
"We have analysed the situation with the coach and we are in agreement that the image we are giving is not of who we really are.
"Pioli will now have to find solutions.
"He is the coach of Bologna and with him we have in the past been able to overcome difficult situations.
"We have to do that again all together."
Pioli joined Bologna in October 2011 and has helped the team retain its Serie A status in the past two campaigns.
Bologna's main problem this term has been in defence, with the Emilia-Romagna club having conceded 20 goals in seven games.
Bologna take on promoted-side Sassuolo on October 20.