Stephen Kenny admitted the Republic of Ireland lacked a cutting edge after Fredrik Jensen grabbed Finland's winner just 19 seconds after coming off the bench in Sunday's Nations League tie.
Kenny is still waiting for his first win since taking charge after a 1-0 defeat in Dublin.
Ireland had rescued a late 1-1 draw against Bulgaria in Kenny's first game in charge on Thursday.
But Jensen's instant impact left Ireland without a victory in League B Group 4 and condemned them to a first ever defeat against Finland, who had been beaten by Wales in their first match in the tournament.
Since replacing Mick McCarthy, Kenny has outlined his plans to turn the Republic into a more possession-based and attack-minded side.
Kenny's decision to use several of the players he worked with as Ireland's Under-21 coach may prove wise in the long run, but it has been a frustrating start to his reign.
He will need a big improvement if Ireland are to qualify for Euro 2020.
A win in the play-offs against Slovakia in October is required to set up a decisive showdown with Northern Ireland or Bosnia in November.
"We had four or five very good chances and when you get them you have to take them. We are disappointed to lose the game," Kenny said.
"There's nothing in the games and the ability to take your chances is critical.
"We've been experimental, I think that's evident, and we wanted players to put themselves in the picture for Slovakia.
"Some players did quite well and it gives us real food for thought ahead of that game."
Norwich striker Teemu Pukki scored 10 times as Finland qualified for Euro 2020 -- their first ever major tournament appearance.
Pukki should have given Finland an early lead when Robert Taylor's pass sent him clean through on goal, but his tame shot was straight at Ireland keeper Darren Randolph.
Shane Duffy appealed in vain for a penalty after tumbling under Juhani Ojala's challenge following an Ireland corner.
Duffy and John Egan both headed over from Robbie Brady free-kicks early in the second half.
Ireland were beginning to get on top and Aaron Connolly drilled into the side-netting before Callum O'Dowda curled just wide.
But it was Finland who snatched the lead with an incisive raid in the 64th minute.
Pukki found down Taylor down the left flank and his low cross reached Augsburg winger Jensen, who slid the ball into the net from close-range.
Callum Robinson had a good chance to equalise when his stinging strike was saved by Lukas Hradecky at the near post.
As Ireland pushed forward for an equaliser, Pukki exploited the gaps at the back and he was denied by Randolph before firing just wide moments later.
Duffy had bagged a late equaliser against Bulgaria, but he couldn't come to the rescue again as the defender nodded over in the closing minutes.