Hazard went down in the early stages at Stamford Bridge but carried on after receiving treatment, though he was eventually taken off in the 65th minute as the Blues held firm to a 4-3 win that sealed a 5-3 aggregate triumph and set up a semi-final against Eintracht Frankfurt.
But Sarri - who saw his side score four in a sensational first half only to concede twice in quick succession after the interval - is confident that Hazard's injury is no major cause for concern.
"Nothing serious, I hope," Sarri told a news conference.
11 - Chelsea are the first English side to win 11 major European games in a single season. Victorious. pic.twitter.com/EJzHBF4fHV— OptaJoe (@OptaJoe) April 18, 2019
"It's only a strong knock. But I think we can recover him for the next match."
Chelsea appeared to be in complete control at half-time at Stamford Bridge, as they had cruised into a 4-1 lead.
But a fine Petr Sevcik brace early in the second period had Slavia on the up and pushing for further goals, as they still needed two more to secure progress to the semi-finals.
Ultimately Chelsea did enough and went through 5-3 aggregate victors, but Sarri was again left baffled by the Blues' second-half woes.
"[Chelsea were] very good in the first half, I think. Really, [we played] very well," he told reporters at his post-match news conference.
"As usual in the last two months, we started very badly in the second half. We need a solution. We need to solve this problem.
"In the last 10 matches, we started like in this match [in the second half]. It's a big problem. We have to concede it's a match for qualification, not for three points, but probably at the end of the first
"But against these opponents, it's not true. They have physical numbers. I have never seen
"The number of accelerations, the metres in high speed, the running... I've never seen anything like that in these opponents.
"So, the second half clearly could be difficult for us, but we did something wrong. In the first 10 or 15 minutes of that half, they scored from 18 metres without being opposed, twice.
"I don't know [why], and it's not easy to understand, otherwise we can solve the problem very easily.
"It's very difficult to understand why. I can try without going into the dressing room at half-time. I can try if that'll solve the problem."