The 24-year-old, who opened the scoring in the game at the Vitality Stadium, was delighted with the way he and his teammates performed against their south coast rivals to move eight points clear of the drop zone.
"I scored one in training this morning and it was nice to do it in the game - I hadn't scored for a while before tonight so it was overdue," said Cook.
"Obviously I'm delighted to score but it's a huge win, we targeted these games to get points early on. It's well documented about our end of season run in, but if we put in more performances like tonight we can beat anyone.
"But we need to carry on and take this performance and result into the Newcastle United game on Saturday."
The Cherries will travel to relegation-threatened Newcastle United on Saturday in their next assignment.