"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.
Doubles from Hakan Calhanoglu and Lautaro Martinez and a late strike from Marcus Thuram extended Inter's advantage on Juventus, who host Sassuolo on Tuesday night.
Italy midfielder Frattesi rammed home the decisive strike in the third minute of stoppage time of an incredible match at the San Siro full of late drama.
Adrien Rabiot's second-half goal earned Juventus a 1-0 home win over AS Roma on Saturday that took them within two points of Serie A leaders Inter Milan.
Yann Bissek's first goal in Italy just before half-time at the San Siro and a late finish from Nicolo Barella were enough for Inter to bounce back from cup defeat to Bologna midweek and keep closest challengers Juventus at bay.
Inter's dynamic attacking duo made sure their team took full advantage of closest rivals Juventus only drawing at Genoa on Friday to put daylight between Simone Inzaghi's side and the rest of the chasing pack
Turkey playmaker Hakan Calhanoglu set up a goal and scored another as Inter Milan moved back to the summit of Serie A with Saturday's comfortable 4-0 home win over Udinese.
Inter Milan scored three second-half goals as they fought back from 3-0 down to rescue a 3-3 draw with Benfica in a pulsating Champions League Group D clash on Wednesday after Joao Mario netted a hat-trick for the hosts.
Inter Milan and Juventus face off on Sunday in a clash between Serie A's two title favourites and historic rivals, as Walter Mazzarri begins his second reign at troubled Napoli.
Lautaro Martinez and Marcus Thuram have rapidly struck up a formidable attacking partnership which will lead Inter Milan into Tuesday's Champions League Group D clash with Salzburg.
Argentina striker Martinez nodded home his 11th league goal of the season in the 67th minute of a straightforward win in Turin as Inter went one point ahead of AC Milan, who host third-placed Juventus on Sunday night.