Captain Scott Brown has urged fans to "keep faith" with Celtic, promising they will return to the Champions League group stage.
There has been disquiet among sections of the support following the failure to qualify this season and last.
With the issue expected to be raised at Friday's annual general meeting, midfielder Brown, 30, promised "we will get there".
He added: "It's been a long two years without Champions League football."
After overcoming three qualifying rounds, Celtic were knocked out of this season's competition at the play-off stage by Malmo.
'We've let ourselves down'
Dropping into the Europa League, the Scottish champions opened their Group A campaign with 2-2 draws with Ajax and Fenerbahce before losing both games against Molde to sit bottom of Group A with two games remaining.
Domestically, Celtic are six points clear at the top of the Scottish Premiership but when asked about how the club are judged more by their European exploits, Brown responded: "It's always going to be that way."
On Celtic's Europa League campaign so far, he said: "We've let ourselves down.
"We know that but we've got two games to go and we can still qualify. Hopefully we can do that with two good performances.
"It's going to be extremely hard. Ajax are a very well organised team. We had a great performance over there, we were a little bit unlucky that we didn't get the three points.
"And Fenerbahce at home, we had a great performance and we lost two slack goals but it was still a good performance.
"It's just the Molde games where we've let ourselves down. I think everyone else can see that we have had good performances against the good teams in the group."
Brown also hopes to finish his career at Celtic and has targeted a domestic treble before he hangs up his boots.
Still hungry for Scotland
Away from club football, Republic of Ireland, who beat the Brown-skippered Scotland to third place in Euro 2016 Qualifying Group D, have progressed to the finals after beating Bosnia and Herzegovina in the play-offs.
"It's hard to take," Brown said.
"We had a great campaign early on. A couple of disappointing results here and there put us out.
"We need to just try and kick on as a nation, be as strong as we possibly can and hopefully try and do as well as we possibly can in the World Cup [qualifiers].
"I'm looking forward to it. A lot of people have been saying I'll be retiring from international duty. I spoke to [Scotland coach] Gordon [Strachan], we had a little laugh about it.
"If it's getting too much for my body, yes [I would retire from Scotland duty] but just now I feel as fit as I've ever been."