The Germans 2-1 semi-final defeat to Italy in Warsaw on Thursday left Joachim Löw's team shell-shocked after the Italians' dominant first-half display yielded two goals from Mario Balotelli to effectively floor Germany.
"For me, there won't be many European Championships or World Cups in the future," said Klose as Mesut Özil's 92nd-minute consolation penalty for the Germans proved too little, too late.
"That's why I'm as disappointed as the rest.
"It's hard to decide now, but I can imagine playing on for two more years to make amends in 2014."
Klose, 34, said the German dressing room was not a happy place after the final whistle and with 64 goals in 121 appearances for Germany, the Lazio man says he wants to play on to help make amends at the next World Cup.
"There is a very sad atmosphere. Some guys are crying and you can only tell them that they have to keep their heads up," said Klose, who is four goals short of Gerd Müller's all-time record for Germany.
"It was one of my bitterest moments, but the hurdle posed by Italy was too high.
"We couldn't play to our potential. Maybe we showed them too much respect."
Italy have maintained their amazing record of having never lost to the Germans in eight meetings at either the European Championships or the World Cup, but midfielder Bastian Schweinsteiger said the young team could only learn.
"We have a very young and talented team and if every player stays on their path, then the (overall) quality will improve for the next tournament," said the 27-year-old.
"It's a positive thing that we've had this experience, especially for the players in their first tournament."
For all their potential and impressive form, Schweinsteiger admits the Germans were found wanting against the Italians.
"They were very clever. Italy are very experienced in terms of the system they play, and it's hard to play against," he said.
"They did very well and managed to score the first goal. It was a mistake to give it away and we didn't manage to equalise.
"The second goal was even worse, and it was hard to find a way back against such an experienced side.
"We lacked a bit of luck and determination, balls bounced off and landed at the feet of the Italians, where it could have landed at our feet, which made it more difficult."
Despite scoring three goals at Euro 2012, Bayern Munich striker Mario Gomez endured a frustrating tournament - indeed he was taken off at half-time of the Italy game after a listless performance - and has yet to bring the consistency of his club form to the international stage.
"Congratulations to Italy, they played an excellent match. We didn't," he admitted.
"It's difficult to find the right words now. "We are very disappointed. We didn't imagine it like this.
"It will certainly take some time to digest all this.
"We all really believed in it and unfortunately once again it didn't happen."
Nearly half a million people had gathered by the Brandenburg Gate in Berlin confident of an all-night party on the back of victory – and could scarcely comprehend the defeat.
"Germany can't lose - it's just not possible," moaned Gina Pusche, a 20-year-old student decked out in a black, red and gold necklace.
"It would have been huge for the people here if their team had won," said Gregory Revel, 51, a metal worker. "You can understand that - the youngsters are really in tune with their team."
In Wolfsburg around 750 Italian fans drove in victory laps around the inner city – where German fans repeatedly tried to stop them. A few scuffles broke out between the opposing sides, and several fans were detained by police for being very drunk.
And in Wuppertal, the derwestern.de newsportal reported German fans threw pasta at Italians after more than 1,000 mixed fans watched the match at an outside public viewing facility.
A confrontation between hundreds of opposing fans was barely controlled by police who used pepper spray to keep the aggressive Germans and Italians apart.