Liverpool's Dejn Lovren reacts after missing the last penalty while Besiktas' players celebrate during the UEFA Europa League round of 32 second-leg match in Istanbul on Thursday. Photo: CFP

A bruised Liverpool will narrow their focus to domestic competitions after being slung out of the Europa League at the round of 32 stage by Besiktas in a thrilling penalty shootout.

Liverpool surrendered a 1-0 lead from the first leg for the game to go to penalties after a goal-less extra time, with Besiktas sneaking through 5-4 after Dejan Lovren's dramatic miss.

"We can just now concentrate on our league campaign, which is now going better, and we have an excellent opportunity in other competitions," said Liverpool manager Brendan Rodgers after the game.

Liverpool's Premier League campaign has now gathered momentum after a dismal start and in the FA Cup they face Blackburn in the sixth round in March.

The side must now also pick itself up for a crunch league clash against Manchester City at the weekend.

"I can only give credit to my ­players," said Rodgers. "­Unfortunately for us Istanbul has not been a happy place for us tonight.

"We are disappointed of course to go out in the manner we did."

With an estimated 70,000 Besiktas fans creating a cauldron-like atmosphere, Liverpool knew they faced a tough task on a balmy February evening at Ataturk Olympic Stadium.

Besiktas leveled on aggregate in the 72nd minute with a stunning strike from Tolgay Arslan, assisted by a deft back heel from Senegalese striker Demba Ba, sending the match into ­extra time and then a penalty shootout.

With penalties level at 4-4 and all the takers holding their nerve, Arslan skillfully slotted in.

Lovren stepped up for Liverpool but his effort went high, leaving the player inconsolable and Besiktas fans running onto the pitch in joy.

"Someone had to miss and unfortunately it was him and us," said Rodgers.

The stadium had special memories for the Reds fans as the scene of the 2005 UEFA Champions League Final where the team famously pulled back a three-goal deficit to defeat AC Milan on penalties.

But Liverpool were this time without talismanic leader Steven Gerrard, who starred on that famous night in Istanbul but is still nursing an injury in his last season for the club.

"We did miss some of our creativity but it's no excuse," said Rodgers.

The famously fanatical black-clad fans of the Eagles worked hard to raise the roof, with deafening whistles every time a Liverpool player touched the ball and dozens of flares burning in the Istanbul night sky.

Banners raised on the stands included "Welcome to hell!" a favorite slogan from Turkish fans for visiting foreign teams.

"It's a great night for our great club, for Besiktas, for Turkish football as well," said triumphant Besiktas manager Slaven Bilic.

He said Liverpool "did not have the creation" but we "definitely deserve it and we are so proud of our players."