Juventus, who missed out on a place in the Champions League knockout stage to group rivals Benfica and Paris St Germain, are ninth in Serie A on 29 points and within 12 points of the top four.
"For me it is a debut on the bench in the Europa League," Allegri told a news conference on Wednesday.
"Our Champions League exit has left us with a bitter taste in our mouths and we're fired up."
In-form Nantes may pose a tough challenge, though, as they have only lost once in their last 12 games - against Marseille - in all competitions.
But Allegri was confident his side could go all the way and lift the Europa League trophy, which would come with a place in next season's Champions League.
"I have great respect for the French team but here we have to lay the foundations that will allow us to go to Nantes with a good lead," the Italian said.
"A new European path begins for us, it is an important objective because it could be a gateway to the Champions League. We want to go all the way."
The pressure will be on Juventus to live up to those expectations if they want to put their off-pitch issues aside following their 15-point deduction in Serie A for false accounting.
"Nantes are a well-organised team that play well. We will have to be just as well organised on the pitch," defender Gleison Bremer (25) added.
"We know the difficulties we are going through but we have closed ranks and reinforced our group spirit."
Captain Leonardo Bonucci (35) returns to the squad having been sidelined since December with a muscle injury, while other players are nearing their return.
"(Juan) Cuadrado and Bonucci have recovered, Leo will also be called up to let him savour the match climate again," Allegri said.
"The only ones out are (Paul) Pogba, Kaio Jorge and (Arkadiusz) Milik.
"We hope to get Pogba back as soon as possible, he trained with the team this morning but he's still catching up. (Federico) Chiesa has recovered well after Sunday's (Serie A) match (against Fiorentina), which is already a positive sign."