"Am I surprised that we are in this situation? No. In this competition if you make one mistake you can be in trouble and that has happened," Benitez told liverpoolfc.tv.
"Because of our past achievements, if we go out now people would say it is the end of something.
"If we cannot win these three games and finish in the UEFA Cup, then we must accept that.
"I am not going to drive myself crazy by thinking about the permutations - you can't do anything about the other teams until you play them. But it is a time to believe."
The prestige of advancing to the latter stages of Europe's elite competition is not the only reason the Reds will be keen to win at home to Turkish outfit, with Benitez admitting that it would also go some way to boosting the Anfield coffers.
"It's important to win in terms of the financial situation," he said.
"We know the Besiktas game is really important but if you approach the game under pressure you will make mistakes. We need to win but we must play with confidence.
"If we qualify it will be much easier with money, but our long-term plan doesn't depend on this competition."