Sunday sees the visit of Spurs in the Barclays Premier League, followed by a trip to neighbours Everton and the visit of impressive leaders Arsenal on October 28.
Sandwiched between the Everton and Gunners matches is their next Champions League trip to Istanbul and a clash with Besiktas.
A tough trip to Blackburn and the Besiktas return are Liverpool's opening games in November.
No wonder Benitez insisted: "We must improve, we must show our character now.
"We know we have to do better. We showed character to get a draw against Porto when we did not play well, and we showed character to win at Wigan last weekend in a hard match.
"Now we must show character against Tottenham. That is our first priority after the Marseille result."