Two years on, and the Newcastle manager's words still stand. Now though, it is Everton who are rubbing shoulders with the likes of Arsenal while the Magpies tread water in mid-table. And on the evidence of last night's 3-0 defeat at St James' Park, the gap is only going to get bigger.
With a vibrancy that is to be expected of a youthful side brimming with pace and attacking talent, Everton closed to within six points of the final Champions League place to cement their status as the likeliest challengers to the current top four.
Ross Barkley, billed as a 'young Paul Gascoigne', opened the scoring with a sensational individual effort that Newcastle's celebrated former son would have been proud of, before second-half goals from Romelu Lukaku and Leon Osman gave the scoreline a more realistic look.
While the visitors were clinical and purposeful throughout, their opponents were devoid of both urgency and an attacking threat.
This was always going to be a critical summer for Newcastle, with Yohan Cabaye still to be replaced, Loic Remy set to leave and question marks over the future of Hatem Ben Arfa and Fabricio Coloccini, but last night's defeat underlined just how much remedial work is required if the likes of Everton are not to disappear over the horizon, let alone a Chelsea or Manchester City.
Newcastle's ongoing lack of success in front of goal brings the continued sidelining of Ben Arfa into sharper focus, and for the second game running, the Frenchman added some much-needed inventiveness and threat when he was introduced shortly before the hour mark. Unlike on Saturday however, last night's game was up before he was on the field.
The reverse fixture at Goodison Park had seen the Magpies blown away by three Everton goals before half-time, and while Roberto Martinez's side were nothing like as effective in the opening 45 minutes last night, it did not take them long to wrest the initiative from their opponents despite a couple of early flurries from Yoan Gouffran.
Martinez inherited a talented squad from David Moyes, but the addition of James McCarthy and Gareth Barry at the base of midfield has made Everton a much more resolute proposition this season, and the visitors' dominance of the central area was a key factor all night.
After Barry won possession in the 18th minute, some slick interplay involving the impressive Gerard Deulofeu and Osman enabled Lukaku to ease beyond Coloccini in the area.
The striker, who scored twice at Goodison, struck a crisp low shot, but Tim Krul got down well to save with his feet.
Four minutes later, and Krul was picking the ball out of his net. Newcastle's defensive inadequacies undoubtedly contributed to the opener, but it would be churlish to take anything away from the individual brilliance of a Barkley goal that is a worthy challenger to last weekend's efforts from Wayne Rooney and Alex Tettey for Goal of the Season.
Barkley was at least ten yards inside his own half when he picked up the ball from Deulofeu's chest-down, but with opponents backing away, he set off an a charge towards the Newcastle goal and kept on running.
Paul Dummett was outpaced from the outset, Mapou Yanga-Mbiwa got nowhere near the Everton midfielder as he cut infield and Coloccini was so flummoxed he slipped onto his backside as Barkley surged into the box.
The run demanded an emphatic finish, and Barkley duly provided it, rifling into the roof of the net from 12 yards.
Newcastle United’s Yoan Gouffran attempts to take the ball off Everton’s Gareth Barry
There have been growing demands for Raheem Sterling and Adam Lallana to make Roy Hodgson's squad for this summer's World Cup finals, but of all the youngsters to have burst onto the scene this season, it is Barkley who is most deserving of a place in Brazil. At the age of just 20, goodness knows how good he could be in the future.
Prior to falling behind, Newcastle had gone close when Papiss Cisse's shot deflected over off Seamus Coleman, and shortly before the break, the hosts threatened again, only for Cisse to be crowded out on the edge of the six-yard box before he could shoot. Despite his match-winner three days earlier, the Senegal international lacked conviction on both occasions.
Gouffran snatched at another half chance two minutes into the second half, and while the Magpies enjoyed a reasonable amount of possession in Everton territory, their attacking players were generally well shackled by a visiting defence that featured another hugely promising youngster in the shape of 19-year-old centre-half John Stones.
As a result, a second Everton goal always looked more likely than a Newcastle equaliser, and it arrived eight minutes into the second half.
Deulofeu broke beyond Dummett down the right-hand side, and Lukaku converted the Spaniard's driven cross from close range.
It was an incisive effort that served to underline the lack of a cutting edge from those in black-and-white, and for the second time in four days, the second-half introduction of Ben Arfa was a tacit acknowledgement of the failing of the midfielders who started the game.
Gouffran drilled a first-time volley narrowly over on the hour mark, and Vurnon Anita should have converted a Ben Arfa cross instead of tugging his shot past the post, but Everton fully merited the third goal that arrived with three minutes left.
Deulofeu rolled the ball to Lukaku, and the Belgian's pass enabled an overlapping Osman to rifle into the roof of the net.