The Italian head coach saw the Russian Premier League leaders come back from conceding two early goals to halve the deficit 12 minutes into the second half.
However, just four minutes after Oleg Shatov had scored, Zenit allowed Robert Lewandowski to restore Dortmund's two-goal advantage, and when Hulk converted a penalty in the 69th minute they again switched off as the Polish striker grabbed his second within two minutes.
The defeat leaves Zenit with a mountain to climb in the second leg in Germany, and Spalletti acknowledged that lapses in concentration may have cost them a chance of progressing to the last eight.
"What bothers me the most - it's the moments in which we make naive and simple mistakes," he said. "Unfortunately, with our team, it happens. In some episodes we lose concentration.
"I believe that in our game, there are moments when we lose a high level of concentration and allow unforced errors, but at this level you pay a heavy price."
Although they face a daunting task in Dortmund on March 19, Spalletti insisted that they could still prevail in the tie and vowed to attack.
"We go there to play with the hope of further output," he added. "In football, as in any other sport game, there is always the opportunity to turn around even the most difficult result.
"It all depends on what you're willing to give in order to achieve results.
"From the perspective of skill, strength, willingness to work, desire to run, the volume of this work.
"Everything is possible. Everything depends on you."
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