The Nerazzurri were obvious favourites considering their strong start to the season, where they have won all their Serie A games and top the table.
Their Czech opponents, however, had other ideas and Olayinka gave them the lead in the 63rd minute, tapping the ball in from Samir Handanovic’s tame save.
It was his first-ever goal in a European club competition. He also became the first Nigerian since Yakubu Aiyegbeni in 2002 to score on his Champions League debut.
The hosts would equalise in the second minute of injury time via substitute Nicolo Barrela, who poked the ball in from a Stefano Sensi’s free-kick that rebounded off the crossbar.
Kwadwo Asamoah was on display for Inter and received a yellow card in the 54th minute for a reckless challenge on Ivorian Ibrahim Traore.
The Ghanaian played the entire 90 minutes and has now featured for a maximum 360 competitive minutes this season.
Antonio Conte will rue his side’s inability to bag a win here as their next European tie is away to Barcelona at the Camp Nou.
They will however return to league action this weekend when they face city rivals AC Milan on Saturday evening.
For the elated Slavia Prague, their next Champions League outing is at home to German heavyweights Borussia Dortmund.
The Czech giants lead the Fortuna Liga and will also tackle city rivals Sparta Prague this weakened.