After a positive opening, the best chance of the first-half came to Finland though when Norwich striker Teemu Pukki found himself in plenty of space. He went one-on-one with Darren Randolph, but the Ireland keeper made an impressive save.
At half time, an even first half saw both teams head into the break all square.
The first score of the game came in the second half as substitute Fredrik Jensen slid a goal in to put the visitors ahead.
With 10 minutes to go, Ireland were left hunting for an equaliser that never came.
Stephen Kenny named a young side for Ireland's match against Finland with an international debut for Brighton midfielder Jayson Molumby.
Three changes were made from the team’s game against Bulgaria, with Harry Arter and Robbie Brady also coming into the side.
In his first game in charge against Bulgaria, Stephen Kenny went for a mix of youth and experience, managing to get a draw after a late header from captain Shane Duffy made it 1-1 at full time.
Their group opponents Wales beat Finland last Thursday 1-0 away from home and this afternoon they beat Bulgaria 1-0.
Meanwhile, Ireland's next game will be a Euro2020 playoff semi-final away to Slovakia on October 8th.
