Liverpool boss Brendan Rodgers says a lack of creativity was one of the main reasons why his team failed to reach the next round of the Europa League.
Taking a narrow advantage from the first leg at Anfield, the Reds battled hard to keep Besiktas out in the first half but were punished when Tolgay Arslan gave the hosts the lead in the 72nd minute, forcing extra-time at the Ataturk Olympic Stadium.
And with the scoreline unchanged after extra time, it was Dejan Lovren who missed Liverpool's fifth penalty, much to the disappointment of his team-mates.
"Over the course of the game, we defended very well and limited them to very few chances," Rodgers said.
"But the one mistake we made, we got punished for, where we just got too deep and they scored.
"Up until they scored their goal, we were quite comfortable in the game. Of course, we're away from home, and the objective for us was to keep a clean sheet.
"We created chances in the first half and in the second half we were comfortable. But we were missing a lot of our creativity this evening.
"But it's no excuse. There were a lot of young players getting great experience with other players who are creative players. We played with two strikers, so it was an attacking line-up.
"And once Besiktas got the goal, we started to have more of the ball again, but we didn't create so much.
"But I didn't think Besiktas created so much either. It was always a tight game, but we just failed to finish the opportunities that we had in the first half.
"We now just have to concentrate on our league campaign that is starting to go well for us.
"Our objective this season was to win a cup. It's not going to be in this competition, but we have an excellent opportunity in [the FA Cup]."