The Parkhead side will face Icelandic outfit Stjarnan – who knocked Motherwell out of last year’s Europa League – in the second qualifying round next month.
Ronny Deila’s men will be favourites to progress as they look to get through three sets of preliminary fixtures to reach the group phase after missing out in 2014-15.
Celtic first-team coach John Kennedy admitted this week that Mackay-Steven was a player signed with European progression in mind when he was recruited from Dundee United in January.
The former Liverpool youngster is adamant that he can deliver as the champions look to join the continent’s elite in the last 32.
He said: “I feel that’s part of my job. I want to play a big part in helping this club qualify for everything and do well in everything.
“I feel ready for that and I’m relishing these opportunities. These are going to be massive games for the club as well as the supporters and for us players too.
“This is why I’m so happy to be here, for the big games. It’s definitely going to be a big task but you’ve just got to enjoy them, play your own game and be confident.
“We’ve got knowledge of them after they played Motherwell last year and they obviously beat them. They were close games and they will be in the middle of their season as well.
“It is going to be very difficult but as soon as I came here, I learned the European stage is where this club belongs and hopefully we can do well in those games.”
Mackay-Steven took time to reflect on a whirlwind first few months at Celtic during his summer holiday and is happy with the impact he has made.
But while many players use their break to get away from their club commitments, he embraced them even more during a break in New York with team-mate Stuart Armstrong.
The 24-year-old winger added: “On the first day we were sitting in a coffee shop when a guy wearing a Celtic top walked past. “He didn’t see us so we thought it would be funny if we went outside. I ran and caught up with him and said in an American accent: ‘Oh my God, are you a Celtic fan?’
“He turned around and was really surprised. He was shocked but it was funny. It was a spur of the moment thing.
“We’d sat for about a second after we’d seen him walk past then I chased him and tapped him on the shoulder. It was the worst American accent ever. He was delighted to see us and we got a picture taken with him. I think he was Scottish and was out on holiday. The fans have been nice with me from day one. It was a little bit of fun. I’m happy to see the fans’ reactions and to engage with them is great. It’s part of the job and I enjoy that side of it.”