The 24-year-old opened the scoring for the Cherries with an acrobatic volley in the 2-0 win over the Saints which marked their first triumph against their local rivals since 1958.
"That result was much needed," Cook said.
"It's an absolutely brilliant result for us against our closest rivals.
"We haven't been great at home and we have needed to improve our home form as it's crucial to us staying in the league.
"It made it sweeter that we could win for the fans against Southampton, who we haven't beaten in the league for 58 years.