Inter fell behind to a surprise goal from Alberto Paloschi in the eighth minute after a defensive lapse between Hugo Campagnaro and Juan Jesus.
Yuto Nagamoto levelled four minutes later for Inter, and had another ruled out as the hosts came right back into the match.
However, despite dominating possession they were unable to find a way past Christian Puggioni in the Chievo goal, leaving Inter with only one win from their past seven league matches.
While the 1-1 draw was disappointing for the head coach his side still moved into fifth place in Serie A, and the 52-year-old was pleased with aspects of their performance.
"I could not have asked for more from my team. We knew Chievo were organised in defence and physically strong, but we had scored to go 2-1 up and had a great chance with Rodrigo Palacio," he told Sky Sport Italia.
"We know that to play good football it takes two teams, but Chievo came here to defend and hope for a mistake to hit us on the counter-attack.
"We did create some scoring opportunities, but missed the final ball and Mateo Kovacic got between the lines but didn't get the right pass.
"Sometimes the ball just doesn't go in and your opponents score at every shot. You just have to keep working. The lads believe in themselves, we just need a little more luck, which is crucial in sport.
"For numerous reasons we have fewer points than we deserve to. If it's our destiny we'll get them back before the end of the season, but if not then we'll just have to see where we end up."
The point was a welcome one for Chievo as it saw them climb a place in the table and put a point between them and the bottom three at the halfway stage of the season.
