Leading by two goals and looking well-placed to advance into the last 16, the hosts were rocked on their heels as Distin lost possession on the edge of the area in the 85th minute and compounded the error by sending striker Liedson sprawling in the area.
Referee Darko Ceferin punished the indiscretion by awarding a spot-kick and dismissing Distin, and Sporting midfielder Miguel Veloso calmly waited for the crestfallen centre back to make his way off before stepping up and sendingTim Howard the wrong way to hand his side a barely-deserved lifeline.
Heaven sent: Steven Pienaar celebrates Everton's opener
Everton had looked good value for a two-goal lead established by Steven Pienaar, on his 100th appearance, and Distin, but Neville was distinctly unimpressed.
Pulling no punches, the Everton skipper insisted his side faced elimination in Lisbon next Thursday unless there was a dramatic overall improvement.
'It was a flat performance,' he said. 'We were not at the same level as in the last couple of weeks, and we did not pass the ball well enough.
'In Europe, you have to take a victory when it comes along, but we are definitely going to have to lift it for the second leg, or we will be out of the competition.
'You think everything is going all right, then one bad mistake gives them an away goal, and they leave with their tails up. We are so disappointed, but it is a lesson for how you have to keep your concentration in Europe.'
Breakthrough: Pienaar slides home Everton's first
The Europa League may have its detractors, and has hardly set pulses racing at Anfield, but the arrival of the knock-out stages was met with enthusiasm on this side of Stanley Park. Sporting were on the back foot from the start and might have been down to 10 men in the 19th minute, but for referee Ceferin giving Daniel Carrico the benefit of the doubt.
A quick word: Everton's Sylvain Distin (left) is consoled by manager David Moyes
After latching on to a Pienaar through ball, Saha appeared to have his heels clipped byCarrico as he went sprawling on the edge of the area. As last man, a free-kick would surely have spelled the end for the Sporting centre back, but Ceferin waved away Everton's protests.
There was no reprieve for Sporting in the 35th minute, though.Neville picked out Cahill with a piercing through ball that sent theEverton forward scampering towards goal.
Mindful, perhaps, that the angle was against him, the Aussie hadthe presence of mind to backheel the ball into the path of Pienaar, whomade no mistake with a first-time finish.
If Rui Patricio excelled with his early double save, he was foundwanting as Everton doubled their lead in the 49th minute.
Baines' deepcorner should have been claimed without too much trouble, even allowingfor Cahill's attempt to mount an aerial challenge.
Instead, the kick sailed over his outstretched hands and hit a startled Distin beforebobbling over the line.
Rui Patricio's claims that he had been impeded quite rightly fell on deaf ears, as Distin somewhat sheepishly turned away to take the congratulations of his team-mates for his second Everton goal since signing from Portsmouth at the start of the season.
Just a second: Tim Cahill rushes to congratulate Sylvain Distin
As commanding as were, they knew a late goal for Sporting would change the entire complexion of the tie. It almost materialised, when Baines denied substitute Carlos Saleiro on the edge of the six-yard area in the 77th minute, and duly arrived soon after in a horror moment for Distin.
MATCH FACTSEVERTON (4-4-1-1): Howard 6; Neville 6, Yyobo 6, Distin 5, Baines 8; Donovan 6, Arteta 6 (Rodwell 78min), Osman 7,Pienaar 7; Cahill 6 (Yyakubu 62, 7); Saha 7 (Bilyaletdinov 83).Sent off: Distin.SPORTING LISBON (4-4-1-1):Rui Patricio 6; Abel 7, Ttonel 6, Carrico 6, Ggrimi 6; Izmailov 7, Mendes 6, Veloso 7, Moutinho 6 (Djalo 67, 6); Fernandez 6 (Saleiro 67, 6); Liedson 6.Booked: Moutinho, Carrico.Man of the match: Leighton Baines.Referee: Darko Ceferin.
After losing the ball on the edge of the area, he barged Liedson tothe ground. Ceferin had little option but to dismiss him, even if hecould have done without Saleiro waving an imaginary card, and leave theway clear for Veloso to strike in a nerveless spot-kick.
Moyes later revealed that Cahill could be doubtful against ManchesterUnited on Saturday, after picking up a calf strain, and added: 'We aredeflated because we haven't seen the job through. We have givenSporting an opportunity they didn't look like getting.
'Sylvain had a very difficult pass to deal with in the build-up tothe penalty, but we should never have put ourselves in that position.We looked more liable to make it 3-0 than concede near the end, but wedidn't take advantage.'
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