Marcos Alonso‘s late goal secured a 1-0 win from a difficult match in Prague.
Sarri said his side have improved from earlier in the season, when they would “immediately concede” in difficult moments.
“In the past we were not able to suffer in the difficult moments of a match,” said the Italian.
“Now we are able to stay in trouble and suffer without conceding.”
An under-strength Chelsea struggled to find any rhythm for large spells, but grew into the game after Eden Hazard was introduced off the bench just before the hour mark.
Alonso timed his run perfectly to meet Willian’s right-wing cross with a firm header four minutes from time at the Eden Arena.
The second leg at Stamford Bridge takes place on 18 April.
Late goal papers over performance
Chelsea return home with a lead, but this was definitely not a vintage European performance from the 2013 Europa League winners.
They were sloppy in possession from the first whistle as Sarri made seven changes from Monday’s dominant victory over West Ham in the Premier League.
Willian hit the crossbar with a fierce shot in the first half, but it took until the 59th minute for Antonio Rudiger to register their first shot on target, moments after Hazard came on.
The Belgian was influential as Chelsea played with more intensity and posed more of a threat, while Willian shot narrowly wide after a neat one-two with Olivier Giroud.
Left-back Alonso had a poor game by his high standards, but popped up with a late run into the area to stun the home crowd.
Chelsea have never lost a European knockout tie having won the first leg away from home, and they travel to Premier League leaders Liverpool on Sunday hoping to make it five consecutive wins in all competitions.
Slavia can pose a threat at the Bridge
Czech league leaders Slavia have scored 10 goals in the knockout stages, and showed enough quality against Chelsea to suggest this tie is not over.
Captain Simon Deli almost handed the hosts an early lead when he headed Miroslav Stoch’s free-kick inches wide at the back post.
Former Blues midfielder Stoch was bright throughout as he pulled the strings for Slavia, who had more shots in total and more on target as they played with an intensity that Chelsea struggled to cope with in the early exchanges.
They almost snatched a goal moments before Alonso’s winner when Ibrahim Benjamin Traore produced a fierce shot at goal, but Kepa Arrizabalaga leapt to his right to save well.
Jindrich Trpisovsky’s side forced Chelsea into mistakes and they will draw confidence from their impressive performances on the road against Genk and Sevilla in the previous rounds.