It was a bright start from Noel King's side as they had plenty of time on the ball, but they struggled to create chances as they could not muster a shot on goal inside the first 15 minutes.
They were punished at the other end as Luka Krajnc knocked the ball into the back of the net after it was delivered from the corner flag in the 13th minute.
Ireland tried to find a response and Callum O'Dowda came close to an equaliser when he unleashed an effort seven minutes from the half-time break, but Grega Sorcan managed to make a stop.
After the break, Jack Byrne tested the keeper by delivering a shot from a free kick on the edge of the box, but it was not powerful enough to get past Sorcan.
Ireland were dealt a further blow when their opponents were awarded a penalty after Sean Long fouled in the box, and it was comfortably taken by Gregor Bajde.
King's side managed to get themselves back into the game when O'Dowda slid the ball under the keeper in the 65th minute, but it did not inspire a comeback.
Seven minutes after conceding, Miha Zaic found the back of the net with a free kick from the edge of the area and wrapped up the win for Slovenia.
Ireland sit fourth in Group 2 after seven games, seven points behind leaders Italy.