Costa was not used at White Hart Lane as Mourinho lost patience with the striker, who tossed his substitutes' bib over his shoulder in the direction of his manager in the final moments of a goalless draw which will do little to kick-start the Barclays Premier League champions' season.
Mourinho said: "If he wants to hurt me, it's not with a bib
I have a good relationship with him, no problems.
"I think Diego is very privileged because he was the last one to be (put) on the bench.
"Everybody was on the bench
I kept him in the team for all these matches and today we thought the best strategy to play was this one
We are happy with the decision."
Costa did not warm up ahead of the game and appeared pitch-side with trainers, rather than boots on, broadcasters sitting near the Chelsea bench reported.
Mourinho says Costa warmed up when instructed to do so.
"A top player going on the bench, they are not happy," Mourinho added.
"For me his behaviour was normal
He was ready to play when they went to warm up."
John Terry, Gary Cahill, Eden Hazard, Cesc Fabregas and others have all found themselves on the substitutes' bench during Chelsea's poor start to the season.
Mourinho said prior to the game that he left out Costa due to low confidence after just four goals this season, but the pair argued at half-time of last Tuesday's Champions League clash in Israel and the manager on Friday criticised the striker's reading of the game.
Reports continue that Chelsea are looking for a new striker in January - with Tottenham's Harry Kane among those linked - and the speculation is likely to heighten after Costa's omission.
Mourinho did not think of turning to Costa in search of a goal which would have secured just a second away win of the season.
"I was looking for the winner, but without him," said Mourinho, who sent on Kenedy and Ruben Loftus-Cheek in the dying moments of the match.
"I was tempted not to touch the team, because the team was dangerous
Why change if we think we cannot improve?"
Mourinho saw reasons for optimism following the performance and praised Hazard as Chelsea's "false nine".
The Belgian forced Hugo Lloris into a second-half save which denied Chelsea victory.
He expects Terry (ankle) and long-term injury victim Thibaut Courtois (knee) to be back for next Saturday's clash with Bournemouth, along with new father Loic Remy and injured pair Ramires and Radamel Falcao.
"The message to every one of my players - not (just) Diego, to every one of my players - when we play as a team and when, especially, we defend as a team, the team is much better," Mourinho added.
"Playing the way we played, I wouldn't be surprised if in the next 10 matches we don't lose one.
"For us the result is not what we want, but the performance is good.
"I think we can look to December with enthusiasm
I'm convinced at the end of December we'll be in a different position to where we are now and we will shorten clearly the distance to the top teams."
Tottenham boss Mauricio Pochettino also did not get the result he wanted as his side extended their unbeaten run to 13 games, their only Premier League defeat this term coming on the opening day at Manchester United.
Pochettino had described the noon kick-off as a "joke" following Thursday night's 2,500-mile flight from Azerbaijan, where his side were in Europa League action.
Asked if he was happy with a draw, in light of the journey to Baku, he said: "No, not really happy
We're a bit disappointed
We deserved more than we got.
"We created enough chances to score
We shot four times on target, and three or four more off target.
"They had one shot on target, in the second half for Hazard
We deserved more in a very difficult game."
Ryan Mason went off with an ankle or Achilles problem and will be assessed early next week.
Source : PA
Source: PA