Paul Lambert's side recorded their third win of the campaign as they shocked the Reds, with Gabriel Agbonlahor scoring the only goal of the game before the Villans showed resilience at the back to keep the clean sheet.
Senderos told the club's official website: "I don't think many teams will come to Anfield and get a win. We showed a lot of character. I thought it was a fantastic performance from everyone.
"From Gabby up front to [Brad] Guzan in goal, everyone did their job brilliantly. We showed brilliant character. Everyone was fighting until the end. It was a great win for us."
Villa are second in the Premier League after four matches of the season.