Federer has been plagued by injury problems this year and the world number three lacked rhythm and confidence in his opening match at this year's grass-court Grand Slam.
The 34-year-old, without a major title since 2012, will play British qualifier Marcus Willis for a place in the last 32.
“I was telling myself how nice it was to be back at Centre Court. I've worked so hard since February to be ready for Wimbledon,” Federer said.
“It was a fun match, it was close, maybe exactly what I needed.
“We'll see if I'm fully fit as I go further in the tournament, nobody knows, not even me.”
Federer's 303rd Grand Slam singles victory moved him within three of Martina Navratilova's record and gave him 302 more wins than world number 706 Willis has managed.
Willis, a 25-year-old tennis coach, defeated Ricardas Berankis, ranked 652 places above him, to win his first ever Grand Slam match and Federer is as fascinated by his fairytale rise as the rest of the tennis world.
“I was very intrigued about his story. It's exactly what this sport needs when guys come from nowhere,” Federer said.
“I'm really excited to play against him. It's a huge moment for him, his story his unbelievable. He was playing club tennis I heard.”
Bidding to win Wimbledon for a record eighth time, Federer would become the oldest man to triumph at the All England Club in the Open era and the oldest Grand Slam champion since Ken Rosewall in 1972 if he lifts the trophy in two weeks time.
Even in the twilight of his career, Federer's pedigree is head and shoulders above most opponents not named Novak Djokovic, but the contrast was especially striking against world number 52 Pella.
The 17-time Grand Slam champion now has 148 victories on grass throughout his glittering career, while Pella had lost all three of his previous matches on the surface and had never been past the second round of any of the four majors.
Yet missing the recent French Open due to a back injury — ending his record run of 65 consecutive appearances in Grand Slams — prolonged a frustrating year for Federer, who also had surgery on a knee injury following January's Australian Open semifinal loss to Djokovic.
TENNIS
Federer wins uninspired Wimbledon opener
Roger Federer was well short of his best as the seven-time Wimbledon champion advanced to the second round with an uninspired 7-6 (7/5), 7-6 (7/3), 6-3 victory over Argentina's Guido Pella on Monday.
ROGER FEDERER
Is this the end of the road for Swiss tennis legend Roger Federer?
Roger Federer is talking optimistically about returning to his "highest level" after knee surgery, but does tennis have to start adjusting to a future without the Swiss star?
The 20-time Grand Slam winner announced on Wednesday that he would be sidelined until 2021 after his second operation in a matter of months.
Federer remains upbeat, tweeting: “I plan to take the necessary time to be 100 percent ready to play at my highest level.”
In some ways 2020 is a good season to miss after the coronavirus ravaged the tennis schedule. Writing Federer off in the past has proved dangerous.
He returned from a six-month injury lay-off to claim the Australian Open in 2017, winning his eighth Wimbledon crown later that year.
But he will be 40 in 2021 and is now heading into uncharted territory.
Despite his groaning trophy cabinet, there are two factors that will motivate Federer to keep going — the risk of losing his grip on the men's Grand Slam title record and a missing Olympics singles gold medal.
Rafael Nadal has 19 majors, just one shy of Federer's mark and Djokovic has 17.
Spain's Nadal will be fancied to draw level with Federer at the French Open, rescheduled for September, while few would bet against Djokovic winning in New York weeks earlier.
In April, Federer said he was “devastated” when Wimbledon was cancelled for the first time since World War II. Last year he fell agonisingly short at the All England Club, failing to convert two championship points on his own serve against Djokovic.
The Wimbledon grass probably remains his best chance of adding to his Grand Slam collection — he has not won the US Open since 2008 and his only title at Roland Garros came in 2009.
Even though Federer has slipped from the very pinnacle of the game, he is still a major threat to Nadal and Djokovic.
'Golden' ambitions
Last year, the world number four had a 53-10 win-loss record and he reached the semi-finals at the Australian Open in January in his only tournament this year.
Federer, who is still six ATP titles short of Jimmy Connors' all-time record of 109, has one glaring omission from his CV — the Olympic title.
The Swiss won doubles gold in Beijing in 2008 with compatriot Stan Wawrinka but lost in the singles final to Andy Murray in London four years later.
The postponed Tokyo Games will almost certainly be Federer's last opportunity to complete a career “golden” Grand Slam — he will turn 40 on the day of the closing ceremony next year.
Tennis will feel the loss of the elegant Federer keenly when he walks off the court for the last time.
Djokovic and Nadal have been the dominant forces in recent years but the Swiss remains the biggest draw and last month topped Forbes' list of the world's highest-earning athletes.
His last appearance on court was in front of nearly 52,000 fans — touted by organisers as a world record for tennis — at a charity match against Nadal in Cape Town in February.
Federer is nearly always the crowd favourite wherever he plays and has proved a perfect ambassador for the sport since he won his first Grand Slam title in 2003.
He certainly expects to be back and competitive next year.
“I will be missing my fans and the tour dearly but I will look forward to seeing everyone back on tour at the start of the 2021 season,” he tweeted.
The avalanche of support from his adoring fans showed they would miss him too, but they will have to get used to a time when he is gone for good.
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