Liverpool are likely to have to beat Porto and Marseille in their final two group games to salvage their qualification ambitions, but Benitez now considers that opponents will be "worried and concerned" about facing the five-times European Cup winners.
Benitez said: "Porto now have to come to Anfield in the next match and they will be worried by this. The rest of Europe will also be aware of what we have done.
"But in the end we still have to win those last two games, regardless of how many goals we scored this time."
Yossi Benayoun grabbed a hat-trick, Ryan Babel and Peter Crouch hit two each with skipper Steven Gerrard grabbed the other goal as the Turkish side collapsed under the pressure of Liverpool's stunning attacking play.
Benitez said: "We have been creating a lot of chances in previous games, but not scoring them.
"Today we scored early and the game opened up. Besiktas also had to win to keep their chances of qualifying going so they had to come out and try to attack and that gave our forwards space to use.
"It made our movement easier, the space was there and our strikers were on very good form.
"But will still must win the next two and then wait to see if it is enough. But we have confidence that we can beat Porto next, and our supporters will also have confidence in us too.
"When you create chances, score hat-tricks and play that well, it gives all the front players - Yossi, Ryan and Peter, plenty of confidence that they can attack and be successful.
"If you score then you have confidence, that is the difference from the way we have played recently.
"But this was an all-round performance by the whole team. Voronin did not score but he was hugely influential in what went on, his play was unselfish and effective.
"He did a tremendous job, and the defence kept a clean sheet so there was very little for me to complain about, just a few minor things."