The team went down fighting after recovering from 3-1 down with nine minutes remaining to find an equaliser in the final seconds of six minutes added time to take the game into extra time.
It took a quite staggering goal to finally knock the stuffing out of the lads as Atud Fokobo walked onto a volley from fully 45 yards that sailed into the top corner for 5-3 in the 102nd minute.
We continued to press and got into some dangerous positions in extra time but couldn't find another goal.
The lads bowed out of competition with their heads held high and will look back at some impressive performances, not least away wins at Barcelona in the group stage and Paris St Germain in the last 16.
The first half came to life in the sixth minute when Alberto Coelho, with his back to goal and seemingly nowhere to go, flicked the ball over Milos Veljkovic and then cushioned a lob over Lawrence Vigouroux.
We took just two minutes to respond. Jack Barthram's cross from the right was missed by Kenny McEvoy but the ball fell into the path of Nathan Oduwa, who smashed home from 16 yards, a sweet strike.
Nabil Bentaleb dragged just wide on 12 minutes and McEvoy was away soon after, speeding into the box from the left channel before looking to sidefoot into the far corner, read by Sporting goalkeeper Mickael Meira.
Sporting were soon back in front though as the dangerous Ricardo Esgaio whipped in a cross from the right and Coelho was there again, launching himself to divert past Vigouroux from six yards.
The game settled and the next chance arrived on 27 minutes when Vigouroux came out of his box to meet a ball over the top but it popped up on landing, allowing Iuri Medeiros to challenge. The ball squirted out sideways and Medeiros just failed to roll back on target.
The final chance of the half fell to McEvoy, played in via Kevin Stewart's fine challenge, the winger looked to beat Meira at the near post but the goalkeeper had it covered.
Chances were few and far between at the start of the second half until Sporting capitalised when Vigouroux was caught out by a ball not skidding through to him, eventually bringing down substitute Alexandre Guedes. Ruben Semedo made no mistake from the spot.
The lads looked down and out at 3-1 as we entered the final 10 minutes but they were handed a lifeline when Coutlhirst was upended by Tobias Pigueiredo and Dombaxe slid home from the penalty spot.
With five minutes left, Barthram's piledriver was spilled by Meira, who recovered just in time before Coulthirst could bundle home.
The comeback was completed as the clock ticked into the sixth minute of added time. Veljkovic played the ball wide to Filip Lesniak and then raced into the box into time to go up for the cross with Meira and Semedo. Meira dropped the ball and substitute Roman Michael-Percil was there to fire into the empty net.
Momentum was with the lads going into the extra half-hour but they didn't get the chance to build on it as Sporting grabbed the lead back in th 96th minute, Guedes' snapshot beating Vigouroux at his near post.
Before they had time to digest that disappointment, Sporting hit them with the hammer blow via the boot of Fokobo, an incredible strike from just inside our half for 5-3.
The lads kept plugging away, Meira denied Coulthirst from close range in the 108th minute, but another comeback from two goals down was beyond even them this time.
Spurs (4-3-3): Vigouroux; Barthram, Ball, Veljkovic, Stewart (D McQueen, 86); Dombaxe, Bentaleb (Onomah, 70), Lameiras (Lesniak, 65); Oduwa (Akindayini, 70), Coulthirst, McEvoy (Michael-Percil, 86). Unused subs: McEnef, Priestley.
Sporting Clube de Portugal (4-1-3-1-1): Meira; Riquicho, Pigueiredo, Semedo, Pinto; Fokobo; Esgaio, Medeiros (Edelino Le, 88), Palhinha (Podence, 88); Rosa (Stojanovic, 73); Coelho (Guedes, 52). Unused subs: Oliveira, Manafa, Martins.