Lagerback is managing at his seventh international tournament in France, having led Sweden in five events before taking charge of Nigeria at the 2010 World Cup.
Iceland are competing in their first major competition and picked up an impressive point against Portugal in their first Group F game, before drawing 1-1 with Hungary.
A win against Austria in Paris on Wednesday will guarantee progression to the round of 16, as well as keeping Lagerback in a job for a few more days – he is due to leave co-coach Heimir Hallgrimsson in sole charge after the Euros.
"I don't know if I will retire totally from football but I definitely will stop with Iceland," Lagerback said.
"Unfortunately, time has come for that I think. I'm not getting younger.
"I have been very privileged with what I have experienced in football with different things.
"Every time you go to the finals it's a real experience. With a national team it's one of the best things you can do.
"Just now I feel really, really good. What these guys have done now - qualified and started the European Championship really well and we have a good chance to go through. For now I think this feeling is the best."
Iceland captain Aron Gunnarsson gave a glowing response when asked if the Austria game was the biggest of his career.
"I can't remember when it was not the biggest game of my career lately," he said. "It's been like that for a while now.
"There's always been pressure on us. Like we said many times before, it's just a question of how we manage to deal with it when we're playing. I'm going to walk proud off the pitch no matter how the game ends. I hope Iceland is proud of us and hope they will be more proud tomorrow."
"It's been a wonderful experience obviously getting the interest that we obviously deserve because we've fought hard to get where we are.
"It all started as young boys and we're here now. But that's not enough in our eyes, we want to go through and we want to qualify because everyone wants to stay here for another couple of weeks.
"If it's possible then happy days, our supporters and the whole world they like the underdogs and it's special to be a part of it."