Zlatan Ibrahimovic's late goal sank Leicester in Sunday's Community ShieldZlatan Ibrahimovic's late goal sank Leicester in Sunday's Community Shield (AFP Photo/Glyn Kirk)
Leicester talisman Jamie Vardy had earlier punished an error by Marouane Fellaini to cancel out FA Cup match-winner Jesse Lingard's first-half solo goal for United, who claimed a record-extending 21st Community Shield.
"It's an important victory, but we have lots of work to do," Mourinho told BT Sport.
"I would be not ambitious if I said it was a fantastic performance. It wasn't. It's always important to start with a trophy."
Mourinho dedicated the win to his predecessor Louis van Gaal, who was sacked after leading United to the FA Cup.
United, who have confirmed they are close to re-signing former player Paul Pogba from Juventus, open their Premier League campaign at Bournemouth next Sunday.
"It feels good," said Ibrahimovic after the traditional curtain-raiser to the English season.
"The first official game, we play for a trophy and we win. Something big is going on with our team."
Leicester manager Claudio Ranieri handed official debuts to close-season signings Ahmed Musa, Luis Hernandez and Nampalys Mendy.
While his side came up short, he was encouraged by the brightness of their display, three months on from their 5,000-1 Premier League triumph.
"I'm very pleased with our performance," said Ranieri. "I watched the same team as last season. Only the result is against us."
Leicester launch their league title defence at Hull City on Saturday.
- Mata flashpoint -
Mourinho deployed his new-look strike partnership of Wayne Rooney and Ibrahimovic and both players made their presence felt in Leicester's penalty area early on.
Rooney headed straight at Kasper Schmeichel from Luke Shaw's cross and the Leicester goalkeeper was also obliged to field a hooked Fellaini shot after Ibrahimovic had leapt to win a high ball.
Leicester attacked the game with the intensity that characterised last season's title triumph and procured several chances of their own.
Vardy drew last-ditch tackles from Daley Blind and impressive United new boy Eric Bailly with trademark darting runs, while Shinji Okazaki glanced a header against the bar from a Marc Albrighton corner.
With Ibrahimovic and Rooney both dropping deep, United lacked an attacking focal point, but in the 32nd minute Lingard took matters into his own hands.
After eluding the sliding Andy King, he drove towards goal, slipped the ball beneath Leicester captain Morgan's sprawling challenge and confidently tucked a shot past Schmeichel.
It came at the same end as his spectacular extra-time winner against Crystal Palace in May's FA Cup final.
Within minutes, United's celebrating fans were singing: "Pogba's coming home!"
Ranieri introduced Musa and Demarai Gray at half-time and the former played a big role in Leicester's 52nd-minute equaliser with an enterprising run from deep.
But the goal owed almost everything to a mistake by Fellaini, whose under-hit back-pass enabled Vardy to nip in, round David de Gea, and score.
Following a glut of changes by both sides, Musa squandered a chance to give Leicester victory when he headed Robert Huth's flick-on over the bar from point-blank range.
Within minutes Ibrahimovic had punished his wastefulness, soaring above Morgan to meet Valencia's cross with a downward header that hit the left-hand post and bounced into the goal.
Henrikh Mkhitaryan made his official United debut as a stoppage-time substitute.
It was Mata who made way, having only entered the fray in the 63rd minute, and the Spaniard, frozen out by Mourinho during their time at Chelsea, exchanged angry words with the United manager as he came off.
Mourinho played down the incident and said he had taken Mata off to help his team defend against long balls.