The former Dundee United player is also adamant that Ronny Deila’s side will find their feet quickly again after returning to training early ahead of the first leg of their second qualifying round clash with FC Stjarnan on July 15.
The Parkhead side resumed training earlier this week and the opening home fixture against the Icelandic title holders will come just seven weeks after they wrapped up last season’s Scottish Premiership-winning campaign.
And Armstrong says the European football he sampled with Celtic last year has left him hungry for more.
He added: “They are very important games, there is no doubt about that but it is more excitement than pressure for us, personally. You grow up watching Champions League games and those are the games you want to play in.
“We had a little taster of European football last season and, personally, I want to taste more.
“We’re back into the swing of things after only three days so we are feeling good and focussing on getting our fitness back.
“With football you take maybe a week or two to get back into your fitness and you don’t get a very long break at all especially with the boys playing international football. I think we will find our feet pretty quickly.”
Armstrong impressed with a string of excellent performances at Tannadice last season before moving to Celtic with United team mate Gary Mackay-Steven in January.
He missed out on a Scotland call up for the national side’s fixtures in March and June, but he is adamant that he is just focussed on Celtic for now.
Armstrong said: “My focus is here and playing well here and doing the best I can for my new club so that is my priority.”