"Now, I feel like crying because we worked so hard, suffered so much, we deserved this joy," the 26-year-old told DAZN.
Inter Milan's Scudetto is easily Inzaghi's biggest honour since winning it as a player with Lazio 24 years ago, and comes after three years of off-field turbulence and serious financial problems which he has navigated with aplomb.
Goals from Francesco Acerbi and Marcus Thuram gave Inter a 17-point advantage over closest challengers Milan and secured their 20th league crown with five matches of the season remaining.
Noah Okafor salvaged a hard-fought point for Milan in the 84th minute on a hot spring day in Reggio Emilia, but second-placed Milan still risk conceding the Scudetto to Inter in a hotly-anticipated derby despite coming back from two goals down.
Italy midfielder Frattesi poked home the decisive goal in the fifth minute of stoppage time in Udine to maintain Inter's 14-point lead at the top of the table with seven matches left in the season.
Monday's comfortable victory left Inter needing just 11 more points from eight matches to beat second-placed AC Milan to a 20th Italian league crown.
Italian club Napoli said they were "stunned" after Italy's football federation (FIGC) on Tuesday dropped a probe into alleged racist comments made by Inter Milan's Francesco Acerbi to Napoli's Juan Jesus due to lack of evidence.
Francesco Acerbi on Monday left Italy's training camp ahead of two friendlies in the United States after reports he will be investigated for alleged racial abuse of Napoli defender Juan Jesus.
Juan Jesus nodded home Napoli's leveller with nine minutes remaining after fighting back from Matteo Darmian's opener shortly before half-time to snatch a deserved point.
Pioli and his players had their heads bowed in remorse while Milan's hardcore ultras bellowed encouragement in the hope that their words might add something which was missing in the first leg. The Milan squad then headed to the dressing room as the Curva Sud chanted “we want 11 lions” in their native Italian.
AC Milan coach Stefano Pioli hopes to have Rafael Leao back for Tuesday's Champions League semi-final, second leg against city rivals Inter in which the Rossoneri will attempt to overturn a 2-0 deficit.
A Romelu Lukaku brace on his 30th birthday, a further strike from Lautaro Martinez and an unfortunate Ruan Tressoldi own goal were enough for Inter to claim a seventh straight win in all competitions and move level on 66 points with second-placed Juventus
"My passion began when I was seven ... I was never able to go, and I had no money," Vanzini, now 100, told Reuters
AC Milan and Inter Milan secured matching 2-0 victories over Roman clubs as they briefly swopped places in Serie A ahead of their Champions League semi-final clash.
Inter Milan came from a goal down to win 3-1 at home against Lazio in Serie A on Sunday, giving Napoli the opportunity to seal their first title since the Diego Maradona era this weekend.
Holders Inter Milan reached the Italian Cup final on Wednesday after beating Juventus 1-0 to go through to next month's showpiece 2-1 on aggregate.
Romelu Lukaku shot Inter Milan to a 3-0 win over struggling Empoli on Sunday with his first Serie A goals from open play since the opening day of what has been a difficult return season in Italy.
Belgian star Lukaku received the ban after picking up two yellow cards, the second for his goal celebration in front of Juventus fans after a stoppage-time penalty which secured Inter a 1-1 Italian Cup draw in Turin two weeks ago
Lukaku, who was sent off in the first leg of the semi-final, will remain suspended for the return against Juventus on Wednesday after the club's appeal was rejected by Italy's Sports Court Of Appeal