The Blues secured a potentially important away goal as they drew 1-1 in Madrid in the first leg, BBC Sport reported.
But Tuchel knows there is plenty more work to do if the London club is to reach a first final since winning in 2012.
"Even if we had won here, everything is possible," he said.
"It's halftime and we'll have to fight for every centimeter and every advantage that we want to have and we need to fight and deserve it."
Christian Pulisic had put Chelsea ahead on Tuesday before Karim Benzema equalized in a thrilling first half.
The second period failed to live up to the excitement of the first, and Tuchel felt his side should have made more of its superiority in the early stages of the game.
"I have a feeling we should have won the first half and that we deserved to win the first half," he added.
"We could have perhaps decided this game in the first half an hour when we were playing so strong."
Timo Werner failed to take a glorious chance to score before Pulisic's opener as his shot from four yards out was saved.
Werner, who has 11 goals in all competitions for Chelsea this season, scored the winner against West Ham in the Premier League at the weekend but also missed a big chance in that game.
"He missed a big one at West Ham and he missed a big one here but it is nothing to cry about," Tuchel said.
"This is the best thing about sport, nobody cares tomorrow. He is maybe angry."
Real Madrid is 13-time winner of the Champions League but boss Zinedine Zidane accepted his side will have to work hard if it is to keep alive the chances of a 14th title.
The Spanish giant travels to Stamford Bridge for the second leg on Wednesday, May 5.
"We're alive and we're going to the second leg with the idea of winning," said Zidane. "In general, we're happy.
"We know they're good in the opposition half, that they're a competitive side and they don't concede many. They're in the semis for a reason."