England bowled out the touring side for 220 on the final day, taking the last wicket with less than 10 overs remaining to win a game that ebbed and flowed over five days.
“It's one of the best matches I've ever been involved in - a great cricket wicket, two sides that gave their all and played as good cricket as they could play,” Cook said at the presentation ceremony.
“I can't really speak. It was just a brilliant, brilliant day.”
It was a great way for England to start the summer ahead of the Ashes series against Australia following a turbulent few weeks off the pitch in which Peter Moores was sacked as coach and the Kevin Pietersen selection saga dominated headlines.
“Let's just enjoy today and what the guys have achieved after a rocky few weeks,” said Cook who played a captain's knock of 162 in the second innings.
New Zealand captain Brendon McCullum was proud of his players.
“I thought we played our part in a tremendous Test match,” he said.
“Great credit to England. Even when we were dominating they kept going and they played an enterprising brand of cricket.
“The game was played in a tremendous spirit too. We got over 730 runs in the test and still lost by more than 100 runs. It's not every day that happens but we hold our heads high. It's such a fine line between success and failure.”
England all-rounder Ben Stokes was named man of the match after scoring the fastest Test century at Lord's to go with a sparkling 92 in the first innings.
He also took the vital wickets of Kane Williamson and McCullum in successive balls on Monday to swing the match England's way.
“He (Stokes) made another massive stride in his development. To score a hundred at Lord's and the way he played in both innings was tremendous for him,” Cook said.
“His challenge will always be to work on his consistency but there is so much talent there and so much desire to win for England he'll only go from strength to strength. We've just got to keep backing him and he'll be a tremendous cricketer.” – Reuters
Original source: Cook hails ‘brilliant’ England victory