Chelsea travel to Premier League champions Manchester City on Sunday with Costa likely to return to the starting line-up after Mourinho opted to select the Spain striker only as a substitute in Wednesday night's 1-1 draw with Schalke in Champions League Group G.
Costa has scored seven times in four Premier League matches this term, but Mourinho says the £32million summer signing from Atletico Madrid is not ready to play more than one game a week after a hamstring problem recurred while on international duty earlier this month.
The City trip is the first of four key domestic fixtures in Champions League weeks for the Blues, who will hope to swiftly find a solution to Costa's niggle.
The trip to Sporting Lisbon is followed by a home clash with Arsenal, Manchester United away follows the Maribor home tie and a date at Liverpool is immediately after the trip to Slovenia.
Didier Drogba started up front for the Blues in Costa's absence, but the hero of the 2012 European Cup win was culpable as Chelsea missed a host of chances to add to Cesc Fabregas' early opener.
Klaas Jan Huntelaar equalised on the counter-attack as Schalke punished Chelsea to earn a point.
Captain John Terry admits Chelsea must address their defensive flaws ahead of Sunday's showdown with City, who will provide a stiff test of the Blues' title credentials after wins over Burnley, Leicester, Everton and Swansea.
Chelsea twice beat City last season, only to finish four points behind them in third place in the final table.
The Blues have conceded six times in the Premier League and Terry was concerned by another leaked goal against Schalke.
"It's disappointing to drop points in the first game at home," the captain said on chelseafc.com.
"The first four league games we've been killing teams off
We didn't do it (against Schalke) but it was disappointing to concede the way we did, from a counter-attack from our own corner.
"It was our corner, we were attacking and we got caught on the break
It shouldn't happen.
"It's the second time already this season it's happened."
Chelsea were beaten by Swiss side Basle in their opening home game last term and responded with four wins to advance.
Mourinho will be keen for early progress in Europe, given the domestic schedule, and Terry is targeting top spot in Group G.
"We lost our first Champions League game last season and we came back to win the group and go through," Terry added.
"We've got some tough games coming up but that's our aim again."
Source : PA
Source: PA