"It's not easy to come out and get out on the centre court," said Federer. "Credit to [Kudryavtsev], I think he did well and obviously it's the best of five [sets] which is hard to keep up maybe. But I played a good match so I'm happy and I'm happy for him too."
The 30-year-old has insisted that he is no longer suffering from a back problem which forced him out of the Qatar Open semi-final earlier this month.
"No problem [with my back]," he added. "I'm happy to be 100% fit. I felt this way for three or four days now. I was a bit worried but I'm here and I'm ready to play."
The Swiss pro will face Andreas Beck in the next round.