A 3-0 series win was wrapped up at The Oval earlier today, although the home side fell 21 runs short of victory as the umpires called time due to bad light.
"It would have been nice to finish with a win but the rules and regulations are there for a reason," Cook said in the post-match ceremony. "The umpires have strict guidelines and, if it was day three, we would have gone off.
"This morning our job was to try and make it as difficult as possible to stop Australia from pushing on for a win and to make our chances of victory easier.
"The crowds have been fantastic for all five tests and I'm privileged to captain this group of guys. Winning this series is the proudest moment of my life."
England take on Australia in the first of two T20 internationals at The Rose Bowl on Thursday.