Davies and fellow youngster Dominic Calvert-Lewin were both handed their first starts of the season by Koeman in Everton's 3-0 victory over Southampton, becoming the first teenage duo to start in a Premier League fixture this term.
Southampton - playing their third match in six days and were without the suspended Virgil van Dijk - has yet to win at Goodison Park since 1997 (4D, 13L).
"It was unlucky [for] the boy that we had to change him but it's true that Enner when he came in... not only to score the goal but his whole performance - we needed his pace in the game". They did not have big chances... maybe at the end from Rodriguez but I think we did well defensively and much better in the second half than in the first.
Baines made it seven points from nine over the Christmas period from the spot after Valencia was fouled by Maya Yoshida and Lukaku's second in three games added gloss to the display.
Southampton, who also suffered an early injury set back when Cedric went off with a head injury, had the ball in the net but striker Jay Rodriguez was adjudged to be offside - and he also used his hand to find the goal.
In what turned out to be an inspired substitution just after the hour mark, the striker, on loan from West Ham, scored then earned a penalty which Leighton Baines converted.
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District Attorney Stan Garnett has said that ruling was not binding and that his office is investigating the case. JonBenet Ramsey was found dead in the basement of her family home in Boulder, Colorado, on Boxing Day 1996.
"It was a really good cross from Seamus and Lukaku controlled the ball well".
Everton's final goal was reward for Lukaku's second-half contribution and evidence of Southampton's lethargy. "He's disappointed but he's young - he will come back".
Former Saints boss Koeman added: "I wasn't happy with the support from the midfield for Romelu in recent weeks".
"It's an opportunity and challenge and a game away against any opportunity we can have the good answer, the necessary quality to win a game".
EVERTON (4-2-3-1): Robles; Coleman, Williams, Funes Mori, Baines; Gueye, Davies; Lennon (Valencia 60), Barkley (Barry 84), Calvert-Lewin (Mirallas 12); Lukaku.