Fernando Torres had given Chelsea an early lead in Istanbul but Aurelien Chedjou netted an equaliser for the Turkish club following a prolonged spell of pressure in the second half.
“I can’t complain. The players were fantastic,” Mourinho told Sky Sports.
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“This is Turkey, this is Istanbul, this is Galatasary, they're very emotional, we were playing against not just a big club but a big club with big players. And it’s not easy.
“We were a bit in trouble. The result is not amazing. The situation in the second leg is difficult.
“If Stamford Bridge can give us 10 per cent of what this public gave them, it would be fantastic for us. I just ask 10 per cent of what this stadium gave to Galatasaray. And we have to try and go through but the second leg will be difficult.”
Mourinho also believes Chelsea’s failure to build on their goal before the break proved costly and feels the fatigue shown by Torres and Andre Schurrle contributed to his side’s second-half display.
“The first half was our game, we had chances to kill the game,” said Mourinho.
“I’m not critical with my striker because my striker had a good game. But overall when we go to counterattack situations, we are missing the last pass, the last control, the last choice.
“Because in the first half we had many occasions to get a second goal, and the second goal would completely change the story of the game.
“My two dangerous players in the first half, Fernando and Schurrle, both were in trouble in the second half.
“Fernando because physically he was exhausted, and Schurrle a bit of that because he’s not playing a lot in the Premier League and because the yellow card put him in a difficult situation.”