The German international said he and his colleagues had to bide their time before they finally broke down a Burnley defence which proved both well marshalled and stubborn.
However, late goals from Nicolas Otamendi and Sane added to Sergio Aguero's first-half penalty secured an 11th-straight win – which equalled a club record for City and put the club five points clear at the top of the table.
And Sane added that that City were playing with both freedom and fun under Pep Guardiola.
"Yes, of course I am very happy that I could help the team with a goal and it was important that we won," said the winger.
"They were very good in their defence. We didn’t have a lot of space in the first half and we were lucky to score with the penalty.
"In the second half we tried to keep the ball more and to play more quickly to score a second goal.
"We try to be at our best in very game. We also try to play and to have fun in the way we play and I think everyone can see that.
"We are very comfortable and we try to keep calm in every game."
Sane also had words of praise for striker Aguero who equalled City's all-time goal-scoring record with that first-half penalty, taking his club tally to 177 goals along with Eric Brook.
"Sergio is a fantastic player. He scores all the time and I am very happy for him to have scored again," said Leroy.