The match was Williams' first singles match in over a year, having been forced to withdraw from last year's Wimbledon due to an ankle injury. She returned to action earlier this month, teaming up with Ons Jabeur at the Eastbourne International as part of her preparation for Wimbledon.
However, things did not go to plan for Williams, who lost a thrilling a three-hour contest against Tan 7-5 1-6 7-6 (10-7). And at the age of 40, some fans believe the time is right for her to retire from the sport as one of its greatest.
"Win or lose @serenawilliams should retire after this @Wimbledon," wrote one fan on social media. "She has had an amazing career. But it's time to call an end to it. What an amazing career. There might never be a better female player"
Another added: "I think it's time for Serena Williams to retire, and that’s okay! She'll always be the GOAT. Nobody can beat her when she’s at her best. #Wimbledon". A third wrote: "Think it's time for Serena Williams to retire now sad to see such a brilliant player look past her best".
When asked about her future following the defeat, Williams remained tight-lipped. "I'm just planning for right now, seeing how I feel, just to go from there," she said.
And when pressed on whether the defeat to Tan will be her last appearance at Wimbledon, she added: "That's a question I can't answer. I don't know. Who knows? Who knows where I'll pop up. There's definitely lots of motivation to play better and at home [the US Open].
"Physically I did pretty good. The last couple of points I was really suffering. If you are playing week in week out there’s a bit more match toughness.
"But I feel like in just those key points, winning some of those points, is always something mentally that you kind of need. I did pretty good on maybe one or two of them, but obviously not enough."