• Lovren misses key penalty in shootout
• Balotelli starts for first time since November
• Scorer Arslan joined Besiktas in January
• Ba hits crossbar at end of normal time
Liverpool lost their first European penalty shootout as Besiktas knocked them out of the Europa League.
Centre-back Dejan Lovren missed the crucial spot-kick after Tolgay Arslan's 20-yard curler forced extra-time in the round of 32 second leg.
Daniel Sturridge's shot was beaten out by Cenk Gonen as Liverpool failed to make their first-half superiority tell.
Besiktas were the better side after that, and almost sealed the tie in 90 minutes as Demba Ba hit the crossbar.
Liverpool had happy memories of their last penalty shootout at the Ataturk Olympic Stadium, where they beat AC Milan to win the 2005 Champions League, but there was to be no repeat here.
Slaven Bilic's side deserved to go through after recovering from a dreadful opening 45 minutes to dominate the game, meaning that Liverpool are left with the FA Cup as their last realistic hope of a trophy this season.
Mario Balotelli played for 82 minutes as he made his first Liverpool start since 8 November, and largely managed to hold his discipline despite an early booking for a foul on Veli Kavlak.
Liverpool were missing a number of injured key players - including captain Steven Gerrard, vice-captain Jordan Henderson, centre-back Mamadou Sakho and playmaker Philippe Coutinho.
But they should have made more of a number of first-half chances, as Raheem Sterling had a shot beaten away somewhat theatrically by keeper Cenk Gonen, then saw a shot on the turn deflected wide by Necip Uysal after Alberto Moreno and Daniel Sturridge had combined to set him up.
Sturridge had Liverpool's best opening before half-time, but took too many touches to cut inside Uysal from the right after being played in by Balotelli, and Gonen beat out the shot.
Besiktas took 41 minutes to get a shot on target, with Simon Mignolet pushing away an effort from Olcay Sahan.
The home side played with more energy in the second period, as Liverpool lost the initiative in midfield - but it was the introduction of former Germany Under-21 midfielder Arslan, signed from Hamburg in January, that gave Besiktas the impetus to get back into the tie.
He gave Rodgers' side a warning with a stunning 35-yard shot that whizzed inches wide of Mignolet's left-hand post.
Liverpool's goalkeeper had no chance when Arslan curled a beautiful shot into the top corner from the edge of the penalty area, after Tore's low ball from the left had been flicked on by Ba.
The former Chelsea striker, having played a part in that goal, should have sent Besiktas through in injury time at the end of 90 minutes, but slammed a shot against the underside of the bar from four yards after Uysal had glanced on a Tore corner.
Ba also had the best chance of extra-time, with Mignolet beating out his shot, before scoring the first penalty of the shoot-out.
Liverpool had won all three of their previous European shootouts, but Lovren put their final kick over the bar after Bilic's side had scored five out of five.
Rodgers: 'Not a happy place for us tonight'
Liverpool manager Brendan Rodgers said: "I can only give credit to my players. Unfortunately for us, Istanbul has not been a happy place for us tonight.
"I think until they scored the goal we were quite comfortable. Our aim was to keep a clean sheet. We did miss some of our creativity but it's no excuse.
"We are disappointed for Dejan Lovren as he had a good game. But someone had to miss and unfortunately it was him and us."
Bilic: 'A great night for Turkish football'
Besiktas coach Slaven Bilic said: "It's a great feeling. It's a great night for our great club, for Besiktas. For Turkish football as well.
"We definitely deserve it and we are so proud of our players."
Mario Balotelli was making his first Liverpool start since 8 November
Balotelli was booked in the 11th minute for a foul on Besiktas midfielder Veli Kavlak
Rickie Lambert, Adam Lallana, Emre Can and Joe Allen scored before Dejan Lovren missed Liverpool's fifth penalty
