Mourinho celebrated his 250th match in charge of the Blues with goals from Oscar and Willian either side of Costa's eighth goal in his first six Premier League games, a tally second only to Micky Quinn's 10 with Coventry 22 years ago.
That is despite the £32million summer signing from Atletico Madrid having a hamstring injury which limits his involvement in training to "almost nothing".
Mourinho said: "I don't care about Diego's goals
For me it's important that the team score enough goals to win.
"I know a striker scoring goals is always nice for him and for his confidence, especially for a player like him who is not training as he should, because we are protecting him in certain situations.
"He cannot be on top of his game, but even so scoring a goal is good for his confidence.
"He's doing almost nothing (in training)
He's just resting and recovering from the tight muscle he has
Every time he accumulates fatigue."
Mourinho believes Costa will only be fully fit if he is given leave from the Spain squad for next month's matches with Slovakia and Luxembourg and fears a hamstring tear if his call is ignored.
"If he doesn't go to the national team and if he stays here 15 days just on treatment, he has the perfect chance to be top for Chelsea and top for the national team," Mourinho added.
"If he doesn't have this period, will be always, plays one game, the other is in trouble, the muscle is tight, the muscle is danger to rupture."
Mourinho has no plans to speak to Spain boss Vicente del Bosque about the striker, who he hopes to select to play Sporting Lisbon in Champions League Group G on Tuesday night.
The Portuguese added: "I want to
Let's see what happens."
Costa has clearly made a big difference to Chelsea.
Mourinho, comparing his side to this time last season, said
"We are a different team
We went in another direction.
"It's a different type of striker we have
He can move, he can come out, he can go to the sides, he can hold the ball
We are a different profile of team."
Mourinho is not aware of Quinn's prowess - "Niall Quinn
He's my generation," the Blues boss said - with Costa top of the Premier League goalscoring charts and his team top of the standings.
Mourinho, chasing his third Premier League title and Chelsea's first since 2010, is refusing to get ahead of himself and believes his side's rivals will not be too concerned by the Blues' position at the summit.
He said: "We go match after match
The next one for the Premier League is Arsenal (next Sunday).
"We have a lead of three points over Southampton, which is a guarantee that next weekend we will still be top of the league.
"Is this very important? It's not crucial because it's too early, but it's a little bit of a space that gives you that good feeling that you're top of the league
It's good to be there.
"Everybody knows the everybody is going to lose points
I don't think any team is scared or convinced that Chelsea's going to keep this run for 10, 15, 20 matches, always getting positive results.
"We know this is the Premier League
Every game is really possible for a top team to lose points."
Chelsea never looked like losing against Villa after Oscar's opener.
Mourinho added: "We kept control of the game all the time
Even when the result was 1-0.
"The second and the third goals obviously killed everything
Overall it was a very good performance."
Villa boss Paul Lambert was content despite a second straight 3-0 loss after the defeat to Arsenal.
"We were well in that game," Lambert said.
"I couldn't fault my own team
We gave it a right good go.
"When you come to places like this, when you get a chance, you've got to score.
"With Nathan's (Baker) header, Fabian's (Delph) couple of shots, (Aly) Cissokho at the back post, you've got to score.
"If you get beat, you've got to leave here with your confidence intact, which we certainly are.
"Performance-wise, other than trying to get a goal, I couldn't ask for any more.
"If somebody said to me you'd take three points from Liverpool, Arsenal, Chelsea, I'd certainly have taken it.
"We're up against Man City next week
Those four teams will be there or thereabouts when the title gets handed out."
Source : PA
Source: PA