Only time will tell whether the Frenchman is right but for the moment, after a first away win since Christmas, his side is in better shape than Everton, who have one point fewer and are currently surveying the Premiership from the discomfort of the bottom three.
There were occasional glimpses of quality from Mikel Arteta and Tim Cahill but largely Portsmouth looked sharper and hungrier. If reports are to be believed - and Portsmouth insist they should not - Perrin's future is in the balance. He should be feeling more secure this morning.
Even so, it was only his third win in 12 matches in charge, which probably accounts for Everton's apparent state of unreadiness as Portsmouth revealed themselves to be better than their results suggest.
Only Nigel Martyn, the Everton goalkeeper, denied them a 10th-minute lead when Gary O'Neil cut back a pass for the debutant Dario Silva to shoot.
The referee, Martin Atkinson, then turned down a reasonable penalty claim when an O'Neil shot appeared to strike David Weir's hand. A restless home crowd made it known they wanted better than this, for all that injuries and suspensions had weakened the hand available to David Moyes. At last, three minutes before half-time, Arteta won a free-kick. Taking it himself, he had Jamie Ashdown at full stretch to turn the ball over.
Portsmouth, though, still threatened, the lively Lomano LuaLua suddenly producing a lob from 25 yards that beat Martyn before rebounding off the crossbar.
That Everton resorted to seeking out Ferguson's head was a clear indication that nothing much else was working. The tactic did almost reward them early in the second half when the Scot put his neck into a powerful header from an Arteta corner. Perrin was relieved to see Richard Hughes stationed on the line to head the ball away.
It was ironic, then, that it should be inside the other penalty area that Ferguson was to provide the afternoon's decisive touch. Assigned the task of tracking Dejan Stefanovic when Laurent Robert whipped in a corner from the right, Ferguson rose with the Serbian defender but managed only to spare him the task of heading it past Martyn.
Moyes went for broke, sending on James Beattie, James McFadden and Leon Osman in a triple change with 25 minutes left, no doubt hoping for a repeat of what happened last January, when Osman's stoppage-time goal won the corresponding fixture. This time, Portsmouth had the last word.
Charitably, Perrin suggested Everton might have had one eye on next Thursday's Uefa Cup trip to Dinamo Bucharest.
A disappointed Moyes was having none of that, however. "That would just be an excuse," he said. "Portsmouth were better than us."
- More about:
- English Football League 1
- Portsmouth FC
- Premier League
- Sir Alex Ferguson
- Tim Cahill