"Everybody knows we are in a difficult moment and scoring goals and winning games is the best medicine to get our full confidence back," Koeman told British media after the match.
"Let's hope the result tonight and the way that we played gives us a boost for Saturday."
Everton have struggled up front after selling Romelu Lukaku to Manchester United, winning just one of their first five league games to lie third-bottom in the table, a point and a place above Bournemouth.
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Koeman was particularly pleased by the performances of Dominic Calvert-Lewin, who scored twice, and Senegal striker Oumar Niasse, who got Everton's third on his first appearance this season.
The decision to start Calvert-Lewin gave Everton an injection of pace up front, with the 20-year-old making a strong case to keep his place against Bournemouth, and Koeman is expecting big things from the England youth international.
"He's always in my mind," the Dutchman said. "He's still a young player, 20, and sometimes you need to protect him. But he's a good player and he will be stronger, he will be faster, he will be better.
"He's doing well and he's a good boy, but we have other players in that position as well."
(Writing by Simon Jennings in Bengaluru; Editing by Amlan Chakraborty)
