In a fairly uneventful game, the hosts just shaded things, however they were punished late on when Emiliano Moretti's header earned the visitors a 1-0 win.
Defeat ended a five-game unbeaten run for Inter in the league and saw them fall eight points behind the top four, although the head coach remained positive about their performance.
"I think we played the right way today," he said. "One failing was that we didn't create enough movement around their penalty box.
"We went to sleep on their goal. We shouldn't have gifted them a corner at that stage of the match and then we were poor in our marking of Moretti.
"But we didn't deserve to lose or even to draw today – we were always on top against a side that defended all game long.
"We just need to roll our sleeves up and work hard because one match doesn't undo all our good work. We're finding our feet.
"Football can be a cruel game, but there's nothing we can do about it. I think we're on the right track."
‘Even though Kevin Keegan was my boyhood hero, we never really saw eye-to-eye. That was an underwhelming time for me – I felt on the outside’: Newcastle cult hero reveals disappointment over how things went under King Kev
Alexander Isak puts uncertainty over his Newcastle United future to bed amid fresh PSG and Arsenal links
