The Iceland international was one of 10 changes made by Gunners boss Mikel Arteta for the 3-0 victory over the Irish champions.
Eddie Nketiah, Joe Willock and Nicolas Pepe scored the goals either side of half-time to make it two wins from two in Group B.
Goalkeeper Alex Runarsson admits he may have to adapt to quiet nights in the Arsenal goal
Runarsson (right) was signed in the summer from Dijon as back-up to No 1 Bernd Leno (left)
The Iceland international made his debut for the Gunners in their 3-0 victory against Dundalk
Runarsson, signed from Dijon in the summer as back-up to Bernd Leno, had to wait until the visit of Dundalk to make his bow.
The 25-year-old conceded 59 goals in 34 Ligue 1 starts for his former club, keeping just five clean sheets in the process.
But he faced only one shot on target during the Dundalk win and, while he may have more difficult tests to come in his Arsenal future, Runarsson knows he will need to maintain his concentration levels for when he is called upon.
‘I think that is normal playing for a club like Arsenal,’ he said when asked if he needs to stay alert when he is not busy.
Runarsson was one of 10 changes made by Arsenal boss Mikel Arteta against the Irish side
‘We have the ball a lot and there are going to be a lot of games like this.
‘But you have to be alert for maybe the one or two chances and I was a little lucky it came at the beginning of the game, it gave me a good start.
‘But I think this is going to be the image of a lot of games for Arsenal.
‘I’m proud to have reached this achievement (making his debut) and I’m proud of the team that we got a very good win. All games in Europe are difficult so it is a very good result.’
Runarsson was not the only player to make their Arsenal debut in the win, as highly-rated young forward Folarin Balogun came off the bench in the second-half.
Runarsson faced just one shot on target but knows he always has to maintain concentration
The 19-year-old came through the ranks with the club and had been linked with a departure in recent months as his contract expires in the summer.
While rumours circulated Balogun was set to turn down any new offer to leave, Arteta said on Thursday that he hopes the teenager has a future at the Emirates Stadium.
Asked about making his debut and what he can offer Arsenal, Balogun replied: ‘It’s been tough.
‘I’ve been at a few other clubs doing trials and stuff like that but I’ve been working my way through the academy and I think as time has gone on I’ve become a better player.
Academy products Joe Willock (left) and Eddie Nketiah (right) were goalscorers on the night
Nicolas Pepe (second from left) also smashed a home a terrific right-foot effort in the match
‘I think that’s shown in my performances and I think it’s good now to get the recognition that my performances deserve.
‘They (Arsenal fans) are going to see lots of energy, and I’d like to say lots of goals.
‘I think I’d like to carry my performances from the youth team into the first team. That’s what got me here so it’s important I carry on playing the way I do.’
Highly-rated young forward Folarin Balogun also made his bow for the Gunners in the win