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 yesterday and cut an isolated figure at times as the holders began their title defence with a 4-1 win.
Chelsea today showed they will be vying with United, who they play a week tomorrow, 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."
The reception was in stark contrast to the one endured by widely unpopular interim boss Rafael Benitez last term.
Mourinho preferred to ponder Roman Abramovich's 10 years as owner, something also celebrated today.
"It's better to focus on that than focus on some negative moments we had in recent history," Mourinho said.
"It's my fifth season I start with Chelsea, it was the first time we had in the dressing room before the match Mr Abramovich with us.
"It's something that means a lot to every group, to every team, at the beginning of the first match at the moment where everybody's together, wishing not just a good match but a good season."
Lampard had a penalty saved by McGregor in the sixth-minute as Chelsea made a fast start, before Oscar's well-worked opener and the England midfielder's blistering second, a 30-yard free-kick.
Mourinho was even content that his team's powers waned in the second half.
"I'm very happy," he said. "I played so many times here, I won so many matches here, but we didn't have so many periods of such fantastic quality like we had (today).
"When I saw the second half growing into another destination, at the beginning I was a bit frustrated because I want more.
"But after five, 10 minutes I was thinking we didn't (give more) because we couldn't - we can't play that way for 90 minutes.
"The three boys behind Fernando (Oscar, Eden Hazard and Kevin de Bruyne) in the first half were fantastic and in the second half they disappeared. All of them they played national team matches.
"The team, when the creativity disappeared, we lost danger in our game."
Hull boss Steve Bruce admitted it was not possible for his side to live with Chelsea in the opening period.
"They were incredible the first 20, 25 minutes," Bruce said.
"With the Special One coming back it was always going to be difficult for us.
"We've got many games to play where we won't be playing Chelsea every week, thankfully."
Bruce has enjoyed a close friendship with Mourinho since signing Mikael Forssell on loan for Birmingham and joked he asked for Lampard in exchange for the Humber Bridge.
New signings Tom Huddlestone and Jake Livermore made their debuts off the bench after joining Hull last week.
"You have to be kind to the players who got you here," Bruce said.
"And believe it or not we've been trying to work on a system to play against Chelsea for two, three weeks."