Usually happy to trot out the usual post-match cliches with a stern expression, Inzaghi had to try his very hardest not to let a huge grin spread across his face as TV pundits on DAZN praised a team they classed as "unplayable" for the rest of Italy's top flight.
Wednesday's emphatic 4-0 win at the San Siro moved Inter 12 points clear of closest rivals Juventus, who are now trailing in the distance after leading the pack little over a month ago.
On Monday night Inter face Genoa on a run of 11 straight wins in all competitions since the turn of the year, their last four in the league coming with four goals.
Inzaghi is closing in on the first league title of his managerial career after narrowly losing last season's Champions League final to Manchester City.
"The team is playing really well but I've been enjoying watching them for two-and-a-half years because we've won five trophies and got to a Champions League final" said Inzaghi.
"I have a team which sticks to its principles regardless of who plays. That had to be the most satisfying thing... whoever comes on it's a pleasure to watch them play. Sometimes I find it hard to pick the team."
Inter have the league's top scorer in Lautaro Martinez and have scored 67 times - more than any team in Europe's top five leagues.
Fans spent the last few minutes of Wednesday's match belting out 'Ole' to their team's every touch as Inter netted four goals without reply for the third straight league match.
Wednesday's clean sheet was their 23rd of the campaign in all competitions, highlighting their dominance of a division in which last season they lost 12 times.
"The final in Istanbul has stayed with us. We missed a great opportunity but it gave us a lot of strength and belief in ourselves," said defender Alessandro Bastoni after the Atalanta win.
"We realised how great it is to play those kinds of matches and how to get there... We were rightly criticised last season because we lost too many games but we, the coach and the staff have bounced back from that."
Inter have a chance to pull even further ahead on Monday as Juve on Sunday travel to Napoli, who finally showed signs of life on Wednesday.
Six goals at Sassuolo, with five coming from hat-trick star Victor Osimhen and Khvicha Kvaratskhelia, gave Napoli their biggest win of the season and hope of European football even though they remain in ninth.
Juve are struggling for results and will be without Adrien Rabiot and Weston McKennie, while Federico Chiesa could also be out after suffering an ankle injury in training on Wednesday.
Player to watch: Victor Osimhen
Osimhen has come back from the Africa Cup of Nations with a bang and his treble against Sassuolo gave Napoli renewed hope of extending a 14-season stay in European competition.
The Nigeria striker is in red-hot form ahead of Juve's visit, scoring five times in three matches in all competitions under new coach Francesco Calzona since returning from Ivory Coast a losing AFCON finalist.
Wednesday's goals were an example of the clinical finishing which has some of Europe's biggest clubs pondering whether to activate his 120 million-euro release clause.
Key stats
12 - Inter's huge lead on Juve.
5 - Osimhen's goal tally in his last three matches.
