The Hoops have one of the toughest groups in the competition, drawing mega-spending Paris St-Germain and five-times European champions Bayern Munich.
They host Bayern on Tuesday seeking a morale-boosting victory at Parkhead.
And despite a receiving thrashing from both Bayern and PSG, Armstrong is adamant Celtic can finish second.
He said: “If we can win on Tuesday night then I don’t see why second place can’t be achievable at all. We have to aim as high as possible.
“Anything is possible. We do not want to put a label on where we want to end up. We take each game as it comes, as boring as it is.
“I know everyone hates it when players say that, but it is true.
“We do not want to think this is where we want to end up, we just need to try and take as many points as we can.”
Celtic were thumped 5-0 at home by PSG on matchday one whilst Bayern put three past them at the Allianz Arena a fortnight ago.
Brendan Rodgers’ side face the German champions at Parkhead tomorrow and if they manage a win they will go level on points in second place.
However, since Jupp Heynckes took over from Carlo Ancelotti last month Bayern have been in irresistible form.
After five successive wins, including a 2-0 win over Leipzig on Saturday, they have been catapulted to the top of the Bundesliga for the first time this season.
Meanwhile, Saturday saw a much-changed Celtic drew at home to Kilmarnock, who have recently been taken over by Rodgers’ former co-worker Steve Clarke.
First-team regulars Scott Brown and Dedryck Boyata were rested by Rodgers, who worked with Clarke under Jose Mourinho at Chelsea during the Portuguese coach’s first spell at the club.
Wing wizard Patrick Roberts will miss the clash, but Bayern will also be without key players Thomas Muller and Franck Ribery.
“I am sure they have very good replacements,” said Armstrong.
“We don’t want to focus too much on them. Okay we will do our research and be focused, but we will focus on ourselves.
“I am sure, whoever they put out, they will be a very strong team.”