When Blackpool last competed in an FA Cup quarter-final, Harold Macmillan was prime minister, the Beatles were yet to be formed and footballers were paid a maximum of £20 a week. Then the Seasiders, winners of perhaps the most dramatic final of all in 1953, were synonymous with FA Cup heroics.

Not now. If they continue to adopt a similar approach to the Cup it may be another 53 years before they grace the last eight.

Times have changed. Promotion to the Premier League is the priority and a Blackpool team stripped of their premier players surrendered the chance of a first quarter-final place since 1959.

Having forged a reputation as endearing, entertaining underdogs during last season's top-flight campaign, they displayed their pragmatic streak here. Ian Holloway made seven changes, the manager deeming Tuesday's Championship encounter with West Ham of greater importance, and his side suffered accordingly.

Depleted before kick-off, defeated after six minutes, they lost to a team whose attitude has never changed. "From the first day of my first year here, we wanted to win a trophy," said David Moyes, approaching his 10th anniversary as manager at Goodison Park.

The 2009 finalists are now 90 minutes away from a Wembley semi-final while Blackpool, in their manager's estimation, belong in a different universe. "We are a million miles away from them," Holloway said. "I thought my team would be better than that."

They were not – and Everton's renaissance continues to gather pace, with the electric, elusive Royston Drenthe lending a sprinter's speed and a craftsman's touch. However, their path into the last eight was rendered simple. While the visitors' understudies floundered, those of the home side flourished.

Everton have long turned adversity to their advantage and did so again. A sick Leighton Baines threw up on the pitch in the warm-up but still played, while the absences of Tim Cahill, Steven Pienaar and Landon Donovan – though the ill American did take to the turf for a final ovation before his loan from LA Galaxy concludes – brought fringe benefits as their deputies excelled.

The new-look side made an immediate impact. Everton struck after 49 seconds, with two of those introduced and one who was relocated in the ensuing reshuffle all contributing. Magaye Gueye broke swiftly, Marouane Fellaini, who was moved into a more advanced role, switched the attack from left to right and Drenthe whipped his shot past Matt Gilks. "Some of their players I've not really heard of," Holloway said. "But their wide leftie [Gueye] was fantastic and Drenthe was fantastic."

The latter was both scorer and supplier. Drenthe's corner was flicked on by Gueye for Denis Stracqualursi, the Argentinian losing his footing as he stabbed his shot over the line.

Given a torrid time by Drenthe, Blackpool's left-back Bob Harris redeemed himself with a goal-saving challenge to thwart Darron Gibson and a goalline clearance to frustrate Fellaini.

"We had six or seven chances to put the game to bed," Moyes said.

Holloway concurred: "It wasn't embarrassing but it could have been a rout." And yet a second-half rally could have given the scoreline a flattering look. After Kevin Phillips's free kick had clipped the bar, Johnny Heitinga bundled Roman Bednar over. But, in a moment to sum up Blackpool's day, Phillips's penalty was struck straight into the Gwladys Street End.

It left Holloway dreaming of a romantic conclusion to this year's FA Cup. "Wouldn't it be nice if Dave [Moyes] won something?" he asked.

"We're desperate to win the final," Moyes said. For Blackpool, however, the major prize is promotion.