Hapoel goalkeeper Yosef Tzur produced a string of important saves at the New Balance Arena, while Charles De Ketelaere's absence and injuries elsewhere left Atalanta short of their usual sharpness in the final third. Speaking to Sky Sport afterwards, Sarri pointed to a squad still finding its rhythm after a demanding summer.
"I expected a difficult match," Sarri said. "It's clear that right now we lack a bit of fluency, we're heavy, we're not yet inside the mechanisms. Every time we receive the ball we think about our position, about what we have to do, and that slows down the fluency of our play.
"But there are also positive aspects: the team is organised, it has played three matches and hasn't conceded a goal.
"I was clear after watching two or three of Hapoel's matches that this would be a complicated game."
Asked about the lack of incisiveness in the final 20 metres, Sarri did not shy away from the shortfall.
"Yes, we lacked a bit of initiative in the final 20 metres, even out wide. We could certainly have done more there. But we're talking about a team under construction, a team that had eight or nine players at the World Cup, so many arrived only a few days ago, and a team with four injuries. In some respects I'm happy and positive, we have to improve in many others."
Hapoel head coach Elyaniv Barda, speaking at his own post-match press conference, struck a satisfied tone despite missing out on a first-leg advantage.
"I congratulate my players," Barda said. "We made it 0-0, but now we have next week's return leg, where we want to do well. We're confident."
He credited his side's approach for keeping Atalanta at bay.
"We played very well today. We didn't just defend the 0-0, we came close to going ahead several times. We put our hearts into it, regardless of the gap in quality between the two teams."
Barda also explained the decision to leave out Turiel, scorer in both legs of Hapoel's previous qualifying round.
"We didn't want to take a risk with Turiel. You always play with 11, and obviously you have to readapt and give everything. The boy was disappointed not to be involved."
The return leg takes place in Miskolc, Hungary, next Thursday, with Atalanta having an extra match, at home to Sassuolo on Sunday, to sharpen their conditioning before then.
"Let's see how we come out of this game and what condition we're in on Sunday," Sarri said. "We take one match at a time. Now it's time to focus on the league, and then from Monday we'll think again about this opponent."