"We could have gone under but instead we reacted. We couldn't have done more than that," Ranieri said. "We played the way we needed to, also tactically. But everything went badly."
"But we won't give up and in the return we can do what they did here," he said.
Shakhtar's Romanian coach Mircea Lucescu was pleased with his side's performance against a Roma side who were jeered by their own fans.
"Roma live under great pressure, I don't understand the fans' jeers, it's tough to play under these conditions," he said.
"In the second half Roma played really well so you can't blame them for anything.
"We also played a great match, we had five players aged 20-21. I knew we'd have to put Roma under pressure and we managed that," he said.