Simone Inzaghi congratulated Milan on their "extraordinary" Scudetto triumph but vowed Inter will come back stronger next season.
Inter beat Sampdoria 3-0 in their final game of the 2021-22 season on Sunday, though it was not enough to stop fierce rivals Milan from claiming a first Serie A crown since 2011.
The Rossoneri had to lose if Inter were to pip them to top spot, but they showed no signs of final day nerves in a comfortable 3-0 win at Sassuolo.
It is only the second time in seven such instances in the three-points-per-win era that Inter have missed out on top spot despite registering 80 points or more.
Their final tally of 84 points were two fewer than Milan managed, with Stefano Pioli's men winning their final five games and going 15 without defeat to conclude the campaign.
While proud of his own side's form in the second half of the season, Inzaghi was quick to praise Milan for seeing out the job.
"Congratulations must go to them because they had an extraordinary season," he told DAZN. "Congratulations to them for managing 86 points.
"Over the last 30 points on offer, we managed three points more than Milan. I am proud of what we have done.
"In February we had a double-header with Liverpool in the Champions League and that had an impact [on our league form].
"Now, in the next few days, we will analyse where we could have claimed the extra victory that would have turned the season from beautiful to extraordinary."
Inzaghi may have fallen just short of retaining the title Inter won last season, but the ex-Lazio head coach won the Coppa Italia and Supercoppa Italiana in his first year in charge.
He is the third manager in Inter's history to win at least 25 matches in his maiden Serie A campaign, after Aldo Olivieri (1950-51) and Jose Mourinho (2008-09).
Reflecting on the campaign as a whole, Inzaghi said: "It has been a challenging journey. But we lifted two trophies and only lost to Liverpool and Real Madrid in Europe.
"Nobody likes being second, but this season will be hard to forget."
Milan and Inter have finished in the top-two spots in successive seasons for the first time ever and will be much fancied to battle it out for the Scudetto again next time around.
After losing a number of key men ahead of this season, Inzaghi is hoping for a positive transfer window to help Inter bounce back in the 2022-23 campaign.
"I'll meet with [chairman Steven] Zhang with a cool head and we'll discuss the future," he said. "We have to do things well because we have fans who deserve to be brought joy.
"[Romelu] Lukaku, [Achraf] Hakimi and [Christian] Eriksen were big losses. We've worked hard to stay competitive and the hope is we can make our squad more competitive."