The Toffees sit eighth in the Premier League table, with Allardyce's long-term future at the club in doubt.
Rooney is expected to leave his boyhood club for America this summer, leaving Allardyce aware of the club's urgency for a new forward.
"The next level of recruitment has to be quality players to get into the team and make them better than what they are at this moment in time," the manager admitted in a press conference.
"There is an area we need to improve and that is goals. Wayne is the leading goalscorer but quite a few of those are penalties so that is the main aim if you are going to finish higher in the league. We still, I think, need another goalscorer that gets 15 or more goals in the Premier League next season because the goal tally has to be at a certain level to achieve sixth and we are way below that level at this moment in time.
"You would need at least two players to be at the 15 mark and you need the midfielders and wide players to be in the sevens to tens. Across the board probably a midfield player and another defender and if there were three high-quality players, that would be enough for Everton to challenge higher up the table."
Everton's final game of the season will come against West Ham United at the London Stadium on Sunday.