The Serie A outfit created numerous chances in the opening 45 minutes and were leading 2-1 at half-time following goals from Mohamed Salah and Federico Fazio.
They struggled after the break, though, and second-half goals from Corentin Tolisso, Nabil Fekir and Alexandre Lacazette saw Roma return home empty-handed.
"We had opportunities to decide the tie already," Spalletti told Sky.
"But we did not take our chances. We were in control, but we were not ruthless enough and eventually suffered toward the end. We could have scored more than two goals, but failed to do so. It will now be a tough task in the return.
"We did not put in a bad performance, but I feel we could have done more. This is a tricky result and makes things difficult.
"But we can still reach the next round. We have to discuss what happened and make some changes. What has happened is in the past now."
The return leg of the last-16 tie will take place at the Stadio Olimpico on March 16.