Inexperienced spinners, all-too-familiar batting collapses and occasional lapses in the field all conspired in their downfall, with the third Test in Sharjah ending in defeat by 127 runs.
They are down to sixth in the International Cricket Council rankings, with another daunting challenge looming away to top-ranked South Africa.
Cook, whose own brilliant form at the top of the order continued, exonerated his seam bowlers. James Anderson and Stuart Broad were hugely skilful and tireless – as was Mark Wood, who missed the third Test with a recurrence of his ankle problem.
Cook felt though that in other crucial areas England were outplayed. He said: “We threw everything at Pakistan for 15 days, with our commitment, our thought, our desire – and in some really testing conditions.
“Our four seamers were outstanding, but the bottom line is we just weren’t good enough with the bat to repel the Pakistan bowlers at crucial times.
“Then with the ball and in the field, we weren’t able to take those tough half-chances – in particular on Wednesday when the game was still alive.”
Man of-the-match Mohammad Hafeez rode his luck, in his second-innings 151.
“Hafeez has scored more than half their runs in that innings,” added Cook. “We had three or four chances to get him – none of them easy – but we weren’t good enough to take them.
“I think that summed up the series. We were there or thereabouts but not quite good enough to put Pakistan under pressure or grab that opportunity ourselves.”
England faltered at the final hurdle, set a target of 284 to win but mustering only 156 all out – despite Cook’s 63 – after losing six wickets for 24 runs.
Perhaps the most jarring contrast of all, though, was how thoroughly Pakistan’s spinners outbowled Moeen Ali, Adil Rashid and eventually Samit Patel.
“Out here you can see the damage their spinners did,” added Cook. “It’s clear at the moment we haven’t got world-class spinners.
“In India in 2012, we had two of the best spinners in the world and won the series pretty much because of Graeme Swann and Monty Panesar.
“We know there’s an issue developing spinners at the moment in England, and I hope there’s a real opportunity for people to push themselves forward in the future.”
Cook gave his team ten for effort on a tour which began in 40-degree heat and cooled off only marginally.
“I can’t fault the lads’ efforts. They’ve been absolutely outstanding,” he said.
Pakistan captain Misbah-ul-Haq warned before the series that England would be much tougher opponents than under Andrew Strauss in 2012.
In victory, he said: “England are one of the top teams, the way they have been playing after winning the Ashes. So winning against them is a big achievement, especially this time because they fought much harder than before.
“They are so disciplined, and don’t give you any easy wickets or easy runs.”
Like England, though, Pakistan must learn to win away too.
“I think our biggest challenge is to play abroad,” added Misbah. “We have to really get ready for that... play differently, plan differently. If we are a very good team, we have to prove ourselves in foreign conditions.”