The hosts made sure of a 3-0 series win at The Oval on Sunday, although the Three Lions fell 21 runs short of victory and a record-breaking 4-0 triumph as the umpires called time due to bad light.
The two sides meet again in Australia in a few months' time, and Anderson feels that England will improve before the next time they face off.
"We know we can go to Australia and play even better. It feels pretty good to win the Ashes," he said last night.
"It would have felt even better if we could have got the last few overs in there. I am delighted to have won the Ashes. Today was fantastic for the crowd.
"As it got closer and closer we really thought we could do it but unfortunately the light didn't hold out.
"But we are going to cherish this moment because it doesn't happen every often."
There were 445 runs scored throughout the day, for the loss of 17 wickets.