The Rossoneri legend was delighted with the 3-0 victory over Celtic on Tuesday and hopes it will act as a catalyst after a poor start to the season.
The Rossoneri defeated Neil Lennon's side thanks to goals from Kaka, Cristian Zapata and Mario Balotelli, moving to within touching distance of reaching the knockout stages in the process.
After a disappointing season so far, which sees Milan currently 13th in Serie A, Baresi hopes the victory will be the start of a good run of form.
"Yesterday Milan produced a good performance," the ex-San Siro defender, voted Milan Player of the Century in 1999, told reporters. "They responded very well after the disappointing result at the weekend [the 1-1 home draw with Genoa].
"More effort in Serie A needs to be shown, but hopefully this will be a good start. The boys were very good in Glasgow."
The current crop of stars just needs to avoid defeat at home to Ajax in its final group game in order to qualify for the last 16 of the Champions League.