Goals from Oscar and Frank Lampard, who also had a penalty saved, saw Mourinho's men triumph in an incident-packed match which saw goal-line technology employed in the top flight for the first time when Allan McGregor saved from Branislav Ivanovic.
Although enthused by the Blues' first-half performance, Mourinho is keen to bolster his squad and is prepared to wait until the September 2 transfer window deadline for Rooney, for whom Chelsea have already had two bids rejected.
"We will try till the last day to add a new player to the squad, a striker, but in this moment every striker has a club, every striker belongs to somebody and I don't think it's ethical that I name players that belong to other clubs," Mourinho said.
"We don't try, like many clubs do, to go around and try to influence players to behave in a certain way. If we have to make a bid, we make it in an official way, we don't speak to players, we speak to clubs."
Rooney featured as a substitute for Manchester United at Swansea on Saturday and cut an isolated figure at times as the holders began their title defence with a 4-1 win.
Chelsea showed they will be vying with United, who they play a week on Monday, for a first championship since 2009/10, but only after Mourinho was welcomed back to Stamford Bridge after a near six-year absence.
Mourinho called for the supporters to now turn their attentions to the team in Wednesday's clash with Aston Villa.
"The reception was amazing," said the self-proclaimed Special One, who acknowledge the adulation by blowing kisses. "I was expecting that because I played here with Inter as an opponent and it was fantastic, so I could imagine that coming to the Chelsea dugout would be like that.
"But when the game started I focused on the game. From now on they have to support the team. We need that every game, especially Wednesday, because we have a very difficult opponent on Wednesday."