Daniel Sturridge opened the scoring for the hosts, before Gary Cahill and Phil Jagielka made sure of the win in front of a sizeable Wembley crowd.
And Hodgson was delighted with the result as focus switches to friendlies against Ecuador and Honduras in the United States in the coming days.
"It was a wonderful send off to the World Cup from a quite incredible crowd," he told ITV. "We had to be very patient but we were dominant throughout and we got our reward.
"It is the perfect end to a perfect two weeks. I am particularly delighted with the way that 85,000-plus people came here to wish us well on our way and that means a lot to us.
"When you play against teams that get 10 men behind the ball ... you have to be patient and keep going, but I was never in any doubt that we would win the game.
"I knew that they would tire and, in the end, I think 3-0 is the minimum we could accept from the game."
Hodgson used the second half to introduce several players off the bench, including giving Everton youngster John Stones his senior international debut.
"When the game was basically over at 2-0, we took the opportunity to change a few of the senior player and give the younger ones a chance," he added.
"I think it's good for them to get out here at Wembley in front of a big and enthusiastic crowd."