The Premier League leaders beat the same opponents 3-0 in both matches at this stage of the UEFA Champions League last season and looked on course to confirm that superiority when Cesc Fabregas put them ahead after 10 minutes in Wednesday's Group G opener.
However, Chelsea missed several good chances to extend their advantage and were then left stunned after 62 minutes when hit on the break by a Klaas-Jan Huntelaar strike.
After scoring seven goals in four Premier League games this term, Mourinho insisted that Costa needed a rest, with Chelsea set to visit title rivals Manchester City in domestic action on Sunday.
The Spain international was brought on after 73 minutes, but Mourinho stated: "He's not in condition to play three matches in a week. He has problems, if he plays one game he needs a week to recover.
"Now playing matches on Tuesday or Wednesday, he can't do it. He wasn't in the right condition. If he had started, maybe after 20-25 minutes I would have had to change him."
Mourinho was predictably frustrated at failing to see off out-of-sorts opponents who are struggling in the Bundesliga, but had no complaints with the result.
"I think we did enough to win," the Chelsea boss claimed on Sky Sports.
"We had great chances to make it 2-0 before they got back to 1-1 and more than a couple of fantastic chances to win the game after they equalised.
"But we have a point, we didn't lose. It isn't the best result, but it is a result and we have a point.
"I remember clear chances for Fabregas in the first half and then Didier Drogba in the second, but we didn't take them and that's football - we have nothing to complain about."
Drogba looked rusty up front and let a few chances go astray before being replaced by the in-form Costa.
Mourinho commented: "He had a good game and made a positive contribution.
"His best chance missed by a matter of inches but he has plenty of experience and is not crying about it."
Chelsea captain John Terry was disappointed both with his side's failure to put the game beyond doubt before Schalke levelled and the manner in which they conceded.
"We were pretty comfortable in the first half, but the manager stressed at half-time that we had started to look a little sloppy and shouldn't throw it away - which is exactly what we ended up doing," said the defender.
"In the first four league games, we've been killing teams off. [Against Schalke] we didn't do that and it's disappointing to concede after we were attacking from a corner. We got hit on the break and it's the second time it's happened this season."
