Benfica secured a Europa League spot after a 3-0 win over Zenit but midfielder Pizzi was frustrated not to progress from Group G.
Lyon's Champions League destiny is no longer in their own hands and Rudi Garcia lamented their defeat to Zenit in St Petersburg.
It will be all to play for on matchday six in Champions League Group G after Zenit returned to winning ways at home to Lyon.
The way Benfica conceded three goals against Zenit left coach Bruno Lage to reflect on "shattered" Champions League aspirations.
Zenit left Lyon with a commendable 1-1 draw on Tuesday and the hosts' head coach pointed to a less than satisfactory start.
Zenit had been linked with Maurizio Sarri but they have appointed Sergei Semak instead, the Russian signing a two-year contract.