Mayo manager James Horan said they won’t be getting carried away with their 21-point win over New York and that they have plenty of room for improvement.
Mayo will remain in the United States until Thursday on a training camp after their facile 1-22 to 0-4 win over the Exiles at Gaelic Park.
They will now go through to face either Roscommon or Leitrim in the Connacht semi-final after dismissing the challenge of a New York side who never got a foothold in the contest played in rainy conditions in front of a record crowd over 6,000 at the Bronx venue.
“Happy enough with some things in the first-half that we did,” said Mayo manager Horan.
He began his initial campaign in charge of Mayo with a hard-earned win over London in Ruislip in 2011.
But this one was never in doubt as they stamped their authority from the outset and cantered home despite shooting 18 wides.
“We just got sloppy, but look, we have won a championship match and we’re into the next round.
“The first-half we set about trying to be ruthless.
"We were strong at times in the first-half but if you contrast that to the second-half we were equally as bad the other way.
“Overall we got through it,” added Horan.