Manchester United rejected two bids from Chelsea for Rooney in the summer transfer window, but the Stamford Bridge club were able to bring in the Cameroon striker from Anzhi Makhachkala on a one-year deal.
Chelsea then moved fellow striker Romelu Lukaku out on a season-long loan to Everton, leaving former Barcelona and Inter Milan star Eto'o to compete with Andre Schurrle, Fernando Torres and Demba Ba for a place in the forward line.
Lukaku spent last season on loan at West Brom, but according to Emenalo the club did not want to pile the pressure on the 20-year-old.
"In the case of Samuel Eto'o, it was an open secret that we wanted Wayne Rooney and I don't need to explain what the idea is behind wanting a player like Rooney," Emenalo told Chelsea's official website.
"But we are not desperate and we know for the future we have Romelu Lukaku and incredible hope that he will come through and lead the line. People keep forgetting that he is only 20, and looking at the short-term plan, we don't want to put too much pressure on a young player like him.
"So if we weren't able to get Rooney and we had Lukaku, Ba and Torres, we felt comfortable with them but we also felt comfortable to bring Eto'o to give us a little bit of competition, because we wanted to freshen up that position."
Chelsea are unbeaten in the Premier League so far this season, but have relied on goals from defence and midfield so far to push them to their two wins, with their most recent result a goalless draw against Man United.
Emenalo added, "We have every confidence in Torres, Ba and Lukaku but with Eto'o we have bought experience."