After an even first half in Reykjavik, the FIFA World Cup Qualifying play-off was turned on its head when Iceland's Olafur Skulason was shown a red card in the 50th minute.
The Zulte-Waregem midfielder dragged back Ivan Perisic 20 yards from goal and, as the last man, was dismissed by the Spanish official.
Croatia used the extra man to dominate possession and created a number of chances, but were unable to beat Hannes Halldorsson in the Iceland goal, meaning the sides head to Zagreb for Tuesday's second leg all square.
Iceland coach Lagerback was proud of the attitude shown by his players, but felt too many decisions went against his team.
"Tonight the referee was not at his best," the Swede said. "I am pleased with the way the players stood up but we were unlucky.
"I did not see a red card from my position, but there were many situations where he (the referee) did not know what he was doing.
"There was a lot of 50-50 decisions that were not in our favour.
"I've seen him a few times and I felt he had a bad day. I also have bad days. That's life."
'William Saliba isn't in the three best centre-backs in the league - I like him, but at the moment, Gabriel is performing better than him and I would love Saliba to get more goals': former Arsenal captain issues challenge to defender
Paul Pogba tipped for sensational Manchester United return this January
