"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.
City are only one step away from being the second English and the eighth European team in history to complete the prestigious continental treble. Tonight, in Istanbul, City will be up against Inter Milan -- “the best Italian team at present,” according to Zlatan Ibrahimovich -- in the Champions League final.
Manchester City are on the brink of a historic treble as Pep Guardiola targets Champions League vindication in Saturday's final against Inter Milan.
Kevin de Bruyne's legacy will not be defined by the outcome of Saturday's Champions League final, the midfielder said ahead of Manchester City's showdown against Serie A side Inter Milan in Istanbul.
Simone Inzaghi's side rose to second in Serie A after winning the Italian Cup on Wednesday with an entertaining win over Atalanta after an early blitz from Romelu Lukaku and Nicolo Barella followed by Lautaro Martinez's simple finish in the 77th minute
Lautaro Martinez scored twice as Champions League finalists Inter Milan came from behind to beat Fiorentina 2-1 and retain their Italian Cup title on Wednesday.
A clash of epic proportions is set to be played out as the Champions League finalists Inter Milan go head-to-head with Conference League finalists Fiorentina tonight in the Coppa Italia final.
Inter Milan coach Simone Inzaghi said he had been impressed by every facet of his team's "extraordinary" journey to the Champions League final after they beat AC Milan 3-0 on aggregate on Tuesday.
A month ago, Inzaghi faced criticism and was under pressure after a lacklustre run of results, yet his side has turned it around and their 1-0 semi-final second leg win over Milan was their eighth in a row in all competitions
Inter will undoubtedly be the underdogs against either Real Madrid or Manchester City in Istanbul on June 10, but the way they managed both legs of this all-Milan tie suggests they will be hard to beat.
Lukaku, on loan at Inter from Chelsea, has struggled with injuries and form this season, but has scored three goals in his last three games