Hamann was brought on as a half-time substitute with the Reds 3-0 down to AC Milan, before Rafael Benitez's side scored three times in six minutes and eventually won the game on penalties.
The German midfielder said that the homecoming in Liverpool city centre the following evening is something that will stay in his mind forever.
"The most memorable thing was when we came back the next day: there were a million people in the streets of Liverpool, in Everton shirts, in Liverpool shirts, just welcoming us home," Hamann told Goal.com.
"It's hard to put into words; people from six months to 100 years old, grown-up people crying in the streets.
"It was just a very touching and emotional moment because if you experience moments like this once, with a club of that history, it will stay with you forever."
Hamann, who scored a penalty in the shootout win over Milan, won nine trophies with the Reds between 1999 and 2006.