Despite benefiting from the goal in the 2-1 win, Bayern coach Louis van Gaal was quick to add his name to the list of those who want some form of aid for officials at top games.
"It was clearly offside," said the Dutchman, refreshingly honest in a situation where many of his colleagues might have simply said they did not see the incident.
"I've been banging on about this for 10 years. There is so much interest in our world of football that we can not any more go without technological assistance.
"This time, we were lucky, but against Girondins Bordeaux in the group stage, we were on the wrong end."
Klose was on his own in the penalty area when he scored from Ivica Olic's headed pass.
Norwegian referee Tommy Henning Ovrebo, at the centre of controversy for his handling of the Chelsea-Barcelona semi-final last season, confirmed the goal amid furious protests from the Italian side.
Bayern said that UEFA president Michel Platini was among the crowd for the match.
The Frenchman has already said he is hopeful the introduction of extra linesmen behind each goal - an experiment being conducted in the Europa League - can help referees without the use of technology.
But with sports such as cricket, tennis and rugby all using some form of technology, it may not satisfy the critics who say that football has become too important to tolerate obvious mistakes that are magnified by television replays.
Last November, there was a huge outcry when French striker Thierry Henry used his hand to set up his team's decisive goal in a World Cup qualifier against Ireland.
The incident took on political overtones with protests outside the French embassy in Dublin.
Fiorentina coach Cesare Prandelli did not want to go into the merits of possible solutions.
"It was a clamorous mistake," he said.
