Everton let slip a one-goal lead at Goodison Park with Nigerian striker Ahmed Musa's second-half brace enough to condemn the Merseyside club to a 2-1 third round defeat and the likelihood of another season without silverware.
"I know what we need to change and if everyone opens their eyes maybe we will get further on our improvement as a team," Koeman told British media.
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"Because that's really what we need and that's all about what happens this month."
Everton have been linked with Manchester United duo Memphis Depay and Morgan Schneiderlin, and Koeman, who will be without injured winger Yannick Bolasie for up to a year, has made it clear to his employers where the team needs to strengthen.
"I have that in mind and the board knows because we spoke together about what we need. That's the job of (director of football) Steve Walsh and it's my job," the Dutchman added when asked about signing new players in the January window.
"I hope everybody realises what the team needs to play and to get results that meet the expectations at this club. I can explain more but I don't like to because that's talks we need to do inside."
Everton, who are seventh in the Premier League after 20 games, host fourth-placed Manchester City on Jan. 15.
(Reporting by Shravanth Vijayakumar in Bengaluru; Editing by John O'Brien)
