The Spaniard now expects to have talks with Foster Gillett, co-owner George's son, who has been installed at Anfield to work alongside chief executive Rick Parry.
Benitez said: "My position is to just enjoy the last game. I have not had the chance yet to talk with Foster Gillett but I will do, and I have also talked again with Rick Parry.
"I hope everything is now behind us. We need to talk about any misunderstanding.
"I have shown my loyalty to the club (over approaches from clubs) and it is clear that I want to stay here, I am really pleased and happy.
"The supporters, players and staff have been excellent and my idea is to keep working just as hard as I have done in the past and try to win trophies for my club. We all want the same thing.
"I said thank you when they bought Fernando Torres, a top-class player, the relationship has been good in the past and must be good again.
"It has been a difficult few days, but I can now say that I am really proud to be here.
"I want to stay here, my commitment to the club is clear. My family is very happy here and I want to win trophies with this club.
"I have had a positive meeting with Rick Parry, we needed to sort out any misunderstandings and talk about the future."