Andy King's goal 13 minutes into the second half on Saturday looked to have given Wales victory in their first game since coach Coleman signed a new two-year contract earlier in the week.
However, Riski brought Coleman and Wales back down to earth when he made it 1-1 by racing onto a fine pass from the impressive Roman Eremenko and beating Wayne Hennessey with a clinical finish in injury time.
Finland had come closest in a drab first half when Celtic striker Teemu Pukki hit the post, but Wales improved after the break and Gareth Bale showed glimpses of his class in his first international appearance since making his world-record switch to Real Madrid in September.
Coleman cut a frustrated figure after seeing his side concede so late in the game and felt they paid the price for switching off.
He told Sky Sports 1: "One slip and we've been caught and we're gutted. The lads are gutted in the dressing room. We thought we’d done enough to win the game, but it wasn’t to be.
"They set the early pace, but I think we worked hard to get back into the game. We got a good goal and we thought it was a penalty (for a push on Simon Church early in the second half).
"You should hold on to that, one slip and we've been punished. One lapse in concentration and you’re punished.
"We learn a lesson and take the positives. I was pleased with boys who came back in and they worked hard."
