Every relegated side can tell a story like this. Stoke City left the pitch with applause ringing in their ears, their supporters summoning a mixture of defiance and appreciation after a performance that deserved more. Paul Lambert had cajoled a full-blooded display that mixed an awareness of their own limitations with moments of genuine threat but it was not enough here and may not be at the end of the season, either.

They lost to a fortunate goal from Christian Eriksen, whose second of the game arrived six minutes after Mame Biram Diouf had equalised via his own piece of luck, and the suspicion is that a lack of quality at either end of the pitch will prove their undoing.

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“I’ve not seen that too many times, you’d have thought we had won the game,” Lambert said of the roars to which his players, some of whom were on their haunches upon Graham Scott’s full-time whistle, departed. It was one of those occasions this stadium creates better than most: raucous, antagonistic and affronted throughout, baying for the most marginal decisions and thundering with noise given the slightest encouragement.

That their efforts were insufficient owed mainly to a free-kick from Eriksen, whipped over from the left flank, that Harry Kane rose to meet but appeared to miss. The ball continued its flight past Jack Butland, who was almost certainly distracted, and as Tottenham’s celebrations unfolded Kane was eager to inform Eriksen that the final touch was his. The Premier League did not agree and Kane, on his return to the starting lineup, will have to live without history recognising any glance off his sleeve.

The goalscorer’s identity dominated the post-match narrative but it is really just a detail. The softness of the concession was of far more concern to Stoke while, for Mauricio Pochettino, the satisfaction arose from a win that makes Champions League qualification look increasingly likely and came without Tottenham looking particularly comfortable. “It puts us in a really good position to achieve what we want,” Pochettino said. “I think it was a massive, massive three points. In football you need some luck but overall we deserved the victory.”

There was certainly cause for satisfaction that, while far from their best, Tottenham’s heads stayed cool. Stoke had lost the sides’ previous four meetings with an aggregate of 17-1 and emerged as if hellbent on turning the tide. They were denied possession for most of the first half but worked feverishly off the ball, the tone set by January signing Badou Ndiaye. The Senegal international looks a bargain at £14m from Galatasaray and his top-flight career should survive any relegation; here he dispossessed Mousa Dembélé twice in the opening quarter with crunching, impeccably timed challenges and denied Son Heung-min an opportunity with a third. Fans and team-mates responded alike: it was not long before Xherdan Shaqiri, tracking back 30 yards to harry Victor Wanyama, brought sections of the crowd to their feet.

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They would have risen in unison had Diouf not jabbed a fine chance over the bar in the 12th minute. That was one of only two first-half openings, the other falling to Son after a lofted pass from Dele Alli. On that occasion Jack Butland saved Stoke but Tottenham’s radar had largely been off.

Butland had no chance when Eriksen, who had been awry before the break, found his bearings. The move started when Bruno Martins Indi, attempting to pass forwards, presented the ball straight to Dembélé and was instantly left floundering when it was slid through to Alli, roaming into the space behind him. Alli had the presence of mind to wait for Eriksen to catch up and his pass was dispatched unerringly.

Stoke refused to fold and equalised when Diouf, racing Hugo Lloris to a delicious Shaqiri pass, scuffed into the vacant net after the Tottenham keeper had belted his clearance against him from point-blank range. This looked like the kind of luck Lambert believes has eluded his team but Eriksen soon provided further cause for regret.

So, too, did the Tottenham crossbar during a rousing finale in which Pochettino admitted Spurs had to “suffer”. It was Shaqiri whose free-kick rebounded from the frame; substitute Tyrese Campbell also headed agonisingly wide 15 seconds after coming on and Diouf, full of running but never wholly reliable, somehow wasted a four-on-one counter five minutes from time.

“I couldn’t ask any more than the way we played,” Lambert says. “Performance-wise, we didn’t look like a team at the bottom.” He believes three victories will secure safety; this was a stirring day’s work but for Stoke, winless in nine, that looks an increasingly long shot.