The Anfield manager watched his side slide to a shattering 2-1 loss against Besiktas in front of a boisterous 30,000-plus crowd in Istanbul.
But a defiant Benitez said: "I was pleased with the performance, but we just could not take our chances.
"When you have 28 attempts on goal as the away side and nearly 60% of possession, that should usually be enough to win the match."
Liverpool were behind on 13 minutes with a Serdar Ozcan effort deflected home off Sami Hyypia.
Benitez added: "We were punished for one mistake in the first half having had so many chances. Their goalkeeper was outstanding but we should have taken more of our chances.
"Obviously it is very difficult now for us to get through but I believe we still can. There are three games left and we must win all three, but we can do that."
Benitez said: "We have to wait to see now what we must do, how the numbers add up. The fact that Porto drew with Marseille in the other group game tonight was a help for us, it certainly improves our options."
He added: "If we continue to play like we did in this match, with so much dominance, we have a chance.
"I do not see this as a test for me as a manager, this is football, if you keep doing the right things like we did here, we will achieve what we want."