Spain striker Costa limped off with a hamstring problem in a pre-season friendly against Barcelona in the U.S., while Cahill suffered a suspected broken nose after scoring an 85th-minute equaliser against the Spanish champions.
"All good, yes," Mourinho told a news conference on Friday when asked about the fitness of Costa and Cahill.
Costa scored 20 league goals for Chelsea in his debut season at Stamford Bridge after joining from Atletico Madrid for 32 million pounds ($50.09 million), but the striker missed large parts of the campaign with a persistent hamstring problem.
Mourinho, however, has no long-term concerns over the 26-year-old's fitness and says Loic Remy and Radamel Falcao will provide Costa with stiff competition during the season.
"No concerns, I am not worried about it," he said. "We have three top strikers. If one is injured we have two more."
The Community Shield, the traditional season-opening match between the Premier League champions and FA Cup winners, has lacked spark on occasions but Mourinho believes the fixture is more than a pre-season friendly.
"It is in between," said the Portuguese, who has not lost to Arsenal manager Arsene Wenger in 13 meetings.
"It is not a friendly... it is more than that but less than a Premier League match."
"I just want my club to get the best possible result. It doesn't matter about Arsenal, it doesn't matter about the manager.
"I never made it an explosion of happiness or special pride in my victories over Arsenal. I do not make a drama if one day we lose."
Goalkeeper Petr Cech ended his 11-year stay at Stamford Bridge to join Arsenal during the close season and Mourinho has no problems with coming up against his former number one having already done so during his time as Inter Milan manager.
"No problem. I did it already, Inter against Chelsea," he said. "I think they have always had very good goalkeepers and now they have one more. I never felt weakness was in their keepers."
($1 = 0.6389 pounds)
(Reporting By Michael Hann; editing by Toby Davis)
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