Benitez said: "It took a long time, but we had to be patient. Maybe it took a penalty, but we'd had several chances before that and dominated the first period."
Liverpool have now stretched their unbeaten start to the season to 16 matches, while Adams will be bitterly disappointed he did not start his Premier League management career with a point, at least.
Tony Adams said: "I was very proud of the side, on another day we may well have come away from Anfield with a 1-0 win.
"We had a couple of great chances, but Liverpool are league leaders and a fantastic team and it is never easy at Anfield.
"Steven Gerrard is one of the best players in the world, but (Lassana) Diarra was exceptional against him. He kept Steven quiet and was still able to get on the ball and play really well to make us tick.
"It is hard to be pleased when we have lost 1-0, but for my first game I am pretty pleased with the performance.
"If they show that level of commitment to me, to themselves and the club we will not go far wrong."