The Nerazzurri needed to beat Sampdoria on the final day and hope AC Milan lost against Sassuolo if they were to pip their fierce rival to top spot.
Inter completed its half of the bargain thanks to a couple of goals for Joaquin Correa after Ivan Perisic had opened the scoring early in the second half.
But it did not matter as Milan was three goals up at half-time against Sassuolo and protected that advantage for a 3-0 win, meaning it – and not Inter – was crowned champion of Italy.
At least three goals had been scored in the previous six league meetings between Inter and Sampdoria, but neither side could find a way through in a relatively low-key first half.
Lautaro Martinez grazed the outside of the post with a header and was thwarted by Emil Audero from the best of Inter's opportunities.
The Inter striker was denied again by Audero after the restart, although Simone Inzaghi's side soon found its groove.
In what could be his final game for the club ahead of his contract expiring next month, Perisic picked out the far corner four minutes into the second half to give his side lift-off.
Correa swept in a first-time finish to double Inter's lead, and the Argentina international added another on the turn two minutes later to completely kill off the contest.
Perisic was carried off on a stretcher after sustaining an injury in the build-up to that third goal, which proved to be the last of the meaningful action on the day Inter's spell as top dogs in Italy officially came to an end.