The Blues, who opened the Barclays Premier League season with a 3-1 win at Burnley, laboured through the first half against the promoted Foxes, back in the top flight after a decade.
After David Nugent was put clean through only to be denied by a smart save from Thibaut Courtois, again picked ahead of Petr Cech, Chelsea eventually made the breakthrough with a well-taken goal from £32million striker Diego Costa.
Eden Hazard stroked in a second on 77 minutes to maintain Chelsea's 100% opening to the new domestic campaign.
Mourinho, though, was not happy with the slow start.
He said: "I prefer to train in the morning, but this week I trained in the afternoon because this is not the best weather to play football, you get lazy.
"This weather pushes players to be a bit lazy, to lose a bit of tension, a bit of sharpness in your body, after that you pass slow, you do not react to the second balls, the time goes on and on, then when you wake up, it is half-time.
"In the first half, the team was lazy, and I did not like that.
"But they improved in the second half and they won, which is the most important thing.
"At half-time, we had to be a bit emotional with them
I told them the way we were playing was not good enough to win the game and that we were at risk
"It is impossible to play football if you do not win one second ball, it was basic but important things."
Mourinho continued: "I told them if you have the same feeling and vision I have, we are not in trouble, because we change, but if you do not agree, we are in trouble and do not win the game.
"In the second half, it was better we were a positive and enthusiastic, so w e were too strong for them
"But let's not forget that they had a one-on-one situation against Courtois."
Mourinho had made another big selection call in leaving striker Fernando Torres out of the match-day squad, which included Didier Drogba who received a warm welcome on his return to Stamford Bridge.
Torres has been linked with a move to Italy, but Mourinho has no intention of off-loading the Spaniard.
"The reason is I decided to keep the same team, to have a bench with a complete balance
Sometimes I can have two strikers on the bench, sometimes I can't," he said.
"I want three strikers in the team
Sometimes I play with two, one on the bench, sometimes someone will be injured or suspended.
"I cannot do a season without three strikers.
"I want him (to stay).
"He will play and score goals, to be very useful for us, he is a fantastic guy, a fantastic professional, so there is no problem."
Costa, signed from Atletico Madrid, opened his account at Burnley, and Mourinho has been impressed by the speed of the Brazil-born forward's transition.
"I got the feeling in pre-season that his adaptation would not be a big deal, he is an easy guy," said Mourinho.
"His style of play has adapted to our needs, so it has not been a problem."
Leicester could count themselves somewhat unfortunate not to have pushed Chelsea harder given their efforts up to the hour mark.
Foxes boss Nigel Pearson feels his side, who drew 2-2 against Everton on the opening weekend, should not be too downhearted.
"The players are disappointed we were unable to convert an encouraging performance with the reward of points, but there are a lot of positives from today," he said.
"The good thing is we created chances throughout the game and we wanted to be positive.
"For the most part, we played very well today, but as always it is going to be about how efficient you are in both penalty areas and we did not quite find the right way today."
Pearson, meanwhile, confirmed there was no further progress on a proposed transfer for Argentina midfielder Esteban Cambiasso, but wants to bring fresh faces in ahead of the September 1 deadline.
The Leicester manager said: "It is not that we have not been trying
It is clear we do need one or two more players, and we will endeavour to add to the squad."
Source : PA
Source: PA