With Carson Yeung and his board of directors watching from the stands, City roared into a 2-0 lead and then survived a belated fightback from Sunderland to ensure that the new regime's reign could celebrate a win.
A delighted McLeish said: "It was more important for me.
"The whole Birmingham City ethos, the fans, the players, everybody associated with the club, it was very important for us.
"It was good. I am pleased for the owners, I am pleased for Carson Yeung and [vice-chairman (football)] Sammy [Yu].
"They are absolutely ecstatic, and so they should be because it was a great home start for them in what was a thoroughly deserved victory."
The home side got themselves in front when defender Liam Ridgewell turned home Sebastian Larsson's 37th-minute free-kick, and doubled their advantage with James McFadden's fine finish three minutes after the restart.
But the home fans among a crowd of 21,723 endured a nail-biting finish after defender Scott Dann put through his own goal, with substitute Fraizer Campbell and Darren Bent passing up late opportunities to snatch a point for the visitors.
However, McLeish's men managed to hang to demonstrate a new-found resilience.
The manager said: "We were 2-0 up against Liverpool two seasons ago and there was a bit of deja vu.
"But the thing about this squad is I believe there's a bit more resilience than we had two years ago.
"We are persevering right to the very end, we are showing that real strength of character when under the cosh.
"On another day, we should probably have been more goals up than the two, but we gifted them a goal and it put us under a bit of pressure.
"But we withstood it and credit to the new players who have come to the club."
The City fans will hope for a major cash investment in the squad as McLeish attempts to secure the club's top-flight status, although the Scot insisted there was no added pressure on them.
He said: "I said to them before the game: 'It's not a dress rehearsal, so enjoy it in the Premier League', and they looked as if they enjoyed their football today.
"But they have got to prove themselves every week. You can say they have nothing to prove, top players, but for me, you go out every week to prove yourself.
"I didn't put any pressure on them and say they were playing for their places. They know on the horizon, there might be new players to augment the squad because we have had problems injury-wise and the fragility of the squad has been evident."
Sunderland boss Steve Bruce did not enjoy his return to St Andrew's two years after his acrimonious departure.
He said: "We didn't really come to the party until the last half hour, that was the disappointing thing.
"In the last half hour, we injected a bit of pace into the game and showed a bit of energy for it, but it was too late.
"In my opinion, you can't play in the Premier League and have six, seven or eight, in the first hour in particular, not at the races or playing poorly or whatever you want to say.
"In the Premier League, you can't get away with it. We nearly did with a couple of wonderful chances, but that's not going to gloss over the first hour where we hit nowhere near the heights.
"The last half hour yes, but it was disappointing, the first hour because we have set ourselves high standards over the last few weeks and basically, we were poor, it has to be said."