"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.
Youngster Kristjan Asllani and veteran Alexis Sanchez scored within six minutes of each other in the San Siro as Inter move closer to going one better than local rivals AC Milan and their Scudetto tally, which would get them a second star above their club badge.
Inter Milan cruised to a 4-0 home win against Atalanta in Serie A on Wednesday, extending their lead at the top of the standings to 12 points as they edge closer to a 20th league title.
Atletico Madrid are hoping Antoine Griezmann's injury is nothing more than a sprained ankle after the forward was substituted in their 1-0 defeat by Inter Milan in the first leg of their Champions League last-16 tie, manager Diego Simeone said.
Inter Milan stretched their lead at the top of Serie A to 10 points on Friday after cruising past sorry Salernitana 4-0 ahead of their Champions League clash with Atletico Madrid.
Juve's title hopes took a hit at the Allianz Stadium in Turin after Lautaro Giannetti poked home the only goal of the game in the 25th minute.
Marcus Thuram was key to Inter's win at a soaking Stadio Olimpico in Rome as, with his team trailing at half-time, the France attacker made it two goals each shortly after the break and forced the Angelino own goal which put Inter ahead in the 56th minute.
Simone Inzaghi's side prevailed in a tense but eventful clash at the San Siro thanks to Federico Gatti's own goal eight minutes before half-time
The Serie A title credentials of Inter Milan and Juventus will be on the line on Sunday as two giants of Italian football face off in a San Siro showdown.
Argentina forward Martinez glanced home the decisive goal in the 14th minute of an action-packed contest in Florence in which Nicolas Gonzalez wasted a late penalty for the hosts, who had Inter on the back foot for much of the game.
Inter Milan will face Napoli in the Italian Super Cup final after comfortably beating Lazio 3-0 in Friday's clash in Riyadh.