"I'm disappointed - we weren't good enough again tonight," 39-year-old Weir told Sky Sports 3 after Tuesday's Group G clash.
"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."
Weir lined up in central defence alongside 17-year-old Danny Wilson and hopes his team-mates will bounce back quickly.
"We've got to take positives from it," said 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."
Manager 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."