Stramaccioni was handed a vote of confidence by president Massimo Moratti after losing 3-1 at Siena, with reports in Italy suggesting he has been given five games to turn Inter's fortunes around.
Croatian teenager Kovacic, who signed from Dinamo Zagreb on transfer deadline day, made his debut from the bench on the ill-fated trip to Tuscany and he has promised to atone for the dropped points.
The 18-year-old told inter.it: "I must admit that we played badly last Sunday, but we'll get back to winning ways and make those three points up.
"I'm very happy to be here, I'm proud to play for such a big club. Who do I aspire to? Robert Prosinecki is my favourite footballer of all time but I like being myself."
Kovacic played both as a playmaker and as a defensive midfielder in Croatia and he believes he can excel in both roles at the San Siro.
"I'm good at both but it's not up to me," he added. "That's the coach's job. What matters is that I give it everything. I really like the tactical side and I think I can offer a lot through the middle."
The Nerazzurri have kept four clean sheets while beating the Flying Donkeys four times in a row and Sunday's visitors have not won this fixture since December 2001.
Luca Castellazzi, Walter Samuel, Dejan Stankovic and Gaby Mudingayi all miss out through injury for Inter while Fredy Guarin and Cristian Chivu serve one-match bans.
Chievo are missing defenders Gennaro Sardo and Boukary Drame while winger Adrian Stoian faces a late fitness test.
Gialloblu head coach Eugenio Corini criticised his players for paying Juventus too much respect during last week's 2-1 home defeat, a result that ended a run of eight games without loss in Verona.
"We know that Juve would arrive with even more determination to win because of their recent poor form," he said.
"We had a great second half but a great Juve side skipped away from us at the end. My lads played really well and they are doing things that we've worked on during the week.
"Unfortunately we didn't get the result but we are happy to have worried them a little."