Both sides' place in Monday's last-32 draw was already secure ahead of a match which Mauricio Pochettino's side approached knowing anything but defeat in Istanbul would see them top Group C.
A decent performance from a much-changed side was not enough to secure them the desired result, though, as a Cenk Tosun goal gave Besiktas a 1-0 win on a night in which Spurs had to overcome play being suspended for the second successive Europa League match.
Play was halted during last month's clash with Partizan Belgrade after three separate individuals encroached onto the at White Hart Lane pitch.
It led to UEFA handing down a 15,000 euros (£11,870) fine just hours before this match, which lasted less than eight minutes before the floodlights failed at Besiktas' temporary home.
Spurs responded strongly to the impromptu break at the Ataturk Olimpiyat Stadium, with Roberto Soldado having several chances, but their inability to find the net allowed Besiktas to go ahead in the 59th minute when Tosun turned home from close range.
Tottenham attempted to level against the Turkish Super Lig leaders and, after another break in play due to a floodlight failure in stoppage-time, the visitors' 18-match unbeaten run in Europa League group matches came to an end.
In theory, it means Spurs will get a tougher draw at the last-32 juncture, as they will face a group winner or one of the best-performing Champions League dropouts - Olympiacos, Zenit, Sporting and Athletic Bilbao.
This was a match for which the build-up was dominated by the omission of one player and the return of another, as Emmanuel Adebayor was given compassionate leave and Kyle Walker made his comeback after a ninth-month injury layoff.
The right-back, fully recovered from a pelvic injury, was part of much-changed Spurs starting line-up in Turkey, where Roberto Soldado the only survivor from Saturday's 0-0 home draw with Crystal Palace.
It did not take the Spaniard long to get involved, with a fizzing Nacer Chadli just evading him - the only moment of note before play was halted.
Just seven minutes and 40 seconds in, the lights suddenly went off at the Ataturk Olimpiyat Stadium and the players were led off the field.
Music blared over the sound system as staff worked feverishly to sort out the issue, with play eventually resuming after a near 17-minute delay.
Spurs returned strongly and, after Chadli saw a tame effort easily held, Besiktas goalkeeper Tolga Zengin did well to stop Soldado turning home from close range.
Ersan Gulum got back to blow the Spain international's next effort on goal, before a scooped Chadli effort found the net - albeit from what was adjudged to be an offside position.
Another Gulum block soon thwarted Spurs, this time cutting out a Soldado cross to Paulinho, and Mousa Dembele had a tame effort during a period in which a hopeful Olcay Sahan strike was all Besiktas could muster.
Serdar Kurtulus had an effort from distance early in the second half but, again, Spurs looked the most likely to find the breakthrough, with Rose forcing Zengin to palm wide.
Besiktas by now, though, were enjoying more of the game and Tosun hit a fine, long-range effort which rattled Michel Vorm's crossbar.
It was a warning shot the visitors failed to heed as moments later Sahan squared impressively for Tosun to turn home from close range.
Soldado had an effort blocked before Rose forced Besiktas captain Zengin into another save as Spurs looked to get back into the match.
However, their attacking focus was leaving them exposed defensively and Tosun wasted a fine chance to wrap up victory, only to hit the side-netting.
Jose Sosa turned over after wriggling free as Besiktas, who ran Arsenal close in the Champions League play-offs, looked to put the game out of sight - before sightlines were lost once more.
Seconds into stoppage-time the floodlights again failed, meaning the players were again forced back down the tunnel for a break.
Spurs piled on pressure when play resumed but could not find an equaliser
Source : PA
Source: PA