The third seed completed a 7-6 (7-5) 7-6 (7-3) 6-3 victory over Argentinian Pella on Monday.
As he continues his return from knee and back injuries, Federer said he was content with how he played on Centre Court.
"I was very happy with the way I played," the Swiss maestro said.
"If I would have used my chances earlier in the first and second sets, maybe things would've been a bit easier.
"But I thought Pella did a good job of playing really good himself.
"It's an intense match, it's a first round, it's new grass so it's always going to be a tough match so I'm happy I made it in straight sets."
Federer needed knee surgery earlier this year and missed the French Open due to a back injury.
The 34-year-old 17-time grand-slam champion said his fitness was slowly improving.
"I haven't played five sets with the new knee," Federer said.
"With every day that goes by, I get away from the back problems I had in Madrid and Rome. It's a good thing so time heals a lot of problems and a lot of issues.
"So it's another day, another step in the right direction and it gives me confidence as I hopefully move forward."
Awaiting Federer in the second round is British qualifier Marcus Willis, who won his first grand-slam match on Monday.