David Weir conceded Rangers didn't deserve to progress.
"I'm disappointed - we weren't good enough again tonight," the 39 year old told Sky Sports 3.
"We didn't play well enough, didn't put enough into the game and got what we deserved.
"It's a hard level to play at and we realise we've got to be better."
"We've got to take positives from it," added Weir.
"Lads are getting good experience, we've got to get better and learn from the experience.
"It's a tough lesson but we've got a big game on Saturday morning against Aberdeen."
Boss Walter Smith echoed Weir's sentiments.
After Rangers also missed out on parachuting into the Europa League, Smith told Sky Sports 3: "We don't deserve it. If we've played three games at home and we don't take a point, we don't deserve to progress.
"Our three home games we've lost now in the Champions League.
"When we're at home and the onus is on us to go forward, we haven't handled it as well as we have in the away games."