Rain meant only 12.2 overs were possible at Lord’s on Monday as the third Test ended in a draw.
But although denied a whitewash, England had already done enough to secure a 2-0 series win after dominant victories by an innings and 88 runs and nine wickets over the Lankans at Leeds and Chester-le-Street respectively.
England now hold Test series trophies against every other major international side except Pakistan, who beat Cook’s men 2-1 in a three-match series in the United Arab Emirates in November last year.
However, they will have a chance to put that right when they face Pakistan in a four-Test series starting at Lord’s on July 14.
“They’ve got a very good (pace) attack, backed up with spinners,” Cook said of Pakistan.
“We’re ready for them. We scored a lot of runs against Australia’s attack here last year – I think it’s going to be a brilliant series.”
While Test specialist Cook prepares for Pakistan, wicket-keeper Jonny Bairstow will be looking to take his red-ball form into the intervening five one-day internationals against Sri Lanka.
Bairstow’s recall into England’s one-day squad was announced just as he was being confirmed as both man-of-the-match at Lord’s and the hosts’ overall man of the Test series too.
His 167 not out in the first innings at Lord’s was his Test-best score and came amidst a series scoring-spree that saw Bairstow total 387 runs at an average of 129, with the Yorkshireman also holding 19 catches behind the stumps.
Together with James Anderson, who took 21 wickets at a stunningly low average of 10.80, Bairstow was the central figure of the series.
Bairstow repeatedly helped England recover from top-order collapses against Sri Lanka and Cook likened his contribution to that of retired former England wicket-keeper Matt Prior.
“He’s very similar to Matt Prior…when he was at his best, we could often be 100 for five and he’d change the momentum,” explained Cook.
Prior’s wicket-keeping came under intense scrutiny early in his career, especially as England – be it Alan Knott, Bob Taylor or Jack Russell – have long prided themselves on their glovemen.
Bairstow, himself the son of the late former Yorkshire and England wicket-keeper David Bairstow, also found his work in the field being called into question after he floored a couple of seemingly straightforward chances against Sri Lanka.
“Jonny is enjoying both roles,” said Cook.
“He knows how hard he has to work at his keeping – that is a conversation we do have,” added the captain, who has been able to observe Bairstow’s work closely from his position at first slip.
Bairstow, meanwhile, was pleased at maintaining the form he showed in South Africa, where his 150 not out in Cape Town in January gave him a maiden Test century.
“Off the back of South Africa, it was important to start the summer well,” he said.
“I hope this is just the start of something that will be special for a while.”
For Sri Lanka captain Angelo Mathews, the hope is his side, having had time to adjust to English conditions, will raise their game in the white-ball formats.
However, the all-rounder accepted England were a much improved one-day team from the side that Sri Lanka thrashed by nine wickets at last year’s World Cup in Wellington.
“They play positive cricket and you have got to be on your toes and really good to beat England in the ODI series that’s coming up,” Mathews said.