"I haven't played as well as I'd like on this tour," said Cook at the presentation ceremony. "I'm working hard on my game, I'm as hungry as ever to score runs.
"You dust yourself off and you go again. I'm captain of my country, yes it hasn't gone well over the last 12 months with my batting in the one-day game, but I would feel very wrong to walk away.
"If that decision gets taken out of my hands then I have to hold my hands up and say I haven't been good enough but until that moment I'll do what I always do," added Cook.
"I'll work incredibly hard. I'm still incredibly hungry to do it."
While England were down in the dumps, Sri Lanka paid a warm tribute to master batsmen Mahela Jayawardene and Kumar Sangakkara after they played their final international match on home soil.
"It's going to be a sad day for all of us," said skipper Angelo Mathews as he looked ahead to the pair's retirement after next year's 50-over World Cup in Australia and New Zealand.
"The service they have rendered over the past 15-16 years has been unbelievable. The encouragement, the guidance they have given to all of us has been amazing."
(Writing by Tony Jimenez, editing by Toby Davis)
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