Cork manager Gerald McCarthy feels his team have room for improvement despite comfortably brushing past Dublin in their hurling qualifier at Parnell Park.
The Munster men were pushed hard during the opening 20 minutes before opening a five point lead at the break. Dublin's challenge wilted after the restart and they allowed their opponents gallop free.
"That was a much tougher game than scoreline suggests," McCarthy said. "But we're very happy with the win. Still, there's vast room for improvement. Dublin deserved to be a lot closer than they were."
"We were a little lethargic in certain aspects of our play which will need sharpening up," he added on RTE television.
"When you're in a good position in a game it's easy to take foot off the pedal. Maybe I'm being a little harsh but that's the way I feel."
The 'Thurles Three' - Donal Og Cusack, Diarmuid O'Sullivan and Sean Og O hAilpin - returned from suspension but their side were slowly into stride.
They gradually picked off points but could not shake off Dublin who stuck doggedly to their task and retaliated with string of fine scores.
Indeed, Joey Boland and John Kelly's respective scores were particularly eye-catching.
Padraig O'Driscoll's point after 22 minutes then levelled the tie at five points apiece. Game on. Dublin were certainly hurling well, but you sensed Cork were just shifting through the gears.
And so it proved as the first of Kieran Murphy's two goals five minutes before the break turned the contest in Cork's favour. With a five point lead at half-time they would never be reeled in.
Murphy scored the other midway through the second half when Joe Deane picked him out with a deft lob before dispatching past goalkeeper Gary Maguire.
Dublin can take tremendous pride in their performance but their second half performance was never strong enough to derail Cork.
The winning 14-point margin was established in injury-time when Patrick Cronin hit the net for the third time in as many championship games.
Eoin Kelly scored 1-12 for Tipperary as Babs Keating's men bounced back from their epic tussles with Limerick to defeat Offaly by four points in Thurles.
Less than 8,000 spectators turned out for a game which Tipperary were only guaranteed of once Lar Corbett found the net in injury time.
Clare beat a spirited Antrim side by eight points in Belfast. Antrim, in fact, had their noses in front for lengthy spells of the opening half but trailed once Daithi O'Connell found the net.
But Niall McManus retaliated with a goal for the home side but even that strike was not enough to prevent Clare leading by six points at the break.
Derek Quinn hit Clare's second goal but Michael Herron's found the net to three points. Niall Gilligan's late goal helped put the result beyond doubt.
SHC qualifying results
Antrim 2-15 Clare 3-21
Dublin 0-15 Cork 3-20
Tipperary 2-17 Offaly 2-13
Laois v Galway, Portlaoise 7pm