Zenit lost 3-1 on the night, but still progressed on aggregate.
"Thanks again - they've been brilliant, as they always are," Reina told Liverpoolfc.com. "They were with us even more when we conceded the goal. That's something to be very happy about and I feel very proud.
"We're disappointed because we didn't get through but we have to be proud of what we did.
"We went out with our heads held high. All we could do was try our best and that's exactly what we did.
"We showed great character, especially after the goal - we just gave our best more than ever. We fought during the 90 minutes for our lives. We showed passion out there.
"We're not happy because we went out but that's football."