Barella volleyed in the rebound after a free kick from Stefano Sensi hit the crossbar.
To be far, Inter were lucky to get a point, as Slavia Prague looked like the team most likely to score for long periods of the match.
With Barcelona drawing at Dortmund, will Inter be left to rue these two dropped points at the end of the group stages?
Inter won their opening three matches in Serie A to open up a two-point lead atop the Italian league but Antonio Conte’s side struggled from the start against the Czech champions, recording only one shot on goal in the first half.
Making matters more difficult, key Inter midfielder Antonio Candreva went off shortly after the break with an apparent injury.
Slavia beat CFR Cluj 1-0 twice in the playoffs to qualify for the group phase, having given eventual champions Chelsea a tough game in last season’s Europa League quarter-finals, losing 4-3 on aggregate.
Slavia’s 23-year-old striker Peter Olayinka was dangerous throughout and put the visitors ahead shortly after the hour mark by turning in a rebound from close range.
Slavia nearly doubled their lead but a free kick from Nicolae Stanciu went just wide and then an attempt from Lukas Masopust sailed high.
Slavia goalkeeper Ondrej Kolar, who was also a key to the success against Cluj, prevented Inter from scoring a late winner when he made a one-handed save to deny Romelu Lukaku’s header in the final minutes of injury time.