"We are AC Milan. We can't afford to sit back and say, let's see what happens," Fassone told media at the club's 'Casa Milan' Friday as he laid out firm objectives a day after the club's takeover.
"The Champions League is a platform a club like Milan can't be without. Four places up for grabs as of 2018-2019, so I won't hide the fact that our aim is to take one of those places.
"That is our aim, but we also want to create a strong and competitive squad."
On Thursday, former Italy prime minister Silvio Berlusconi ended a remarkable 31-year reign as the club's owner and president when he sold the legendary Serie A side to Rossoneri Sport Investment Lux.
The €740 million ($786 million) deal, dogged by months of delays, sees mystery Chinese businessman Yonghong Li - whose €500m fortune reportedly comes from the construction and packaging businesses - named as Milan's new president.
It also sees Milan become the second Chinese-owned club in the city. Bitter rivals Inter, who host Milan at the San Siro on Saturday, are owned by the Chinese group Suning.
Milan emerged as the world's top team during their 1990s heyday when the likes of Marco van Basten, Ruud Gullit, Frank Rijkaard, Franco Baresi and Paolo Maldini created the blueprint for Rossoneri teams for the best part of 20 years.
But Milan won their last Champions League title in 2007, their last scudetto in 2011 and haven't competed in the Champions League since 2014, when they were ousted 5-1 on aggregate by Atletico Madrid in the last 16.
Newly-appointed president Li said in Chinese: "AC Milan is a top global club with 118 years of history. In the Berlusconi reign alone Milan won eight league titles, five Champions League titles and seven Italian Super Cups.
"This has left supporters with big expectations for the club. We know we shoulder a huge responsibility, but we want to surpass those expectations and make sure fans are shouting 'Forza Milan!' (Let's Go Milan) all over the world.
"Last year we shared our vision with Mr Fassone. We fully trust him and the team he has put in place.
"We are sure that with his support, AC Milan will get better and better. We want the club to be competitive ... in all competitions."
With Champions League qualification now virtually out of Milan's hands for next season -- Vincenzo Montella's men sit sixth at 20 points behind leaders Juventus and 10 behind Napoli in third place -- the club is targeting the 2018-2019 season.
Serie A has already been assured by European football's ruling body Uefa they will have a fourth Champions League spot, as opposed to the three currently available, two of which offer automatic tickets to the group stages.
In the meantime, Milan will look to boost their Europa League qualifying hopes with a win away to Inter on Saturday, when a global audience is expected to watch the first all-Chinese 'Derby della Madonnina' at 1130 GMT.
And for Fassone, a former director with Juventus and Inter Milan, it couldn't get better.
"From an emotional and emotive point of view, we couldn't ask for anything better," added Fassone.