The American, appearing at the championships for a record 24th time, retains the easy power that once made her the queen of Centre Court but went down 6-4, 6-3.
"Grass is inherently going to be slippery. You're going to fall at some point. It was just bad luck for me," former world number one Williams told reporters later.
"I started the match perfectly. I was literally killing it, then I got killed by the grass."
Williams, whose last Wimbledon title was in 2008 against sister Serena, won the opening two games but looked in serious trouble in the next as her bandaged right knee buckled under her while she moved to intercept a volley.
The Centre Court crowd winced as she crumpled to the turf, but after staggering back to her chair and receiving treatment the old warrior spirit kicked in and she battled on.
"I'm not sure what I've done. I'm going to have to investigate it tomorrow. It's late today. But it was quite painful," she said.
Svitolina, who at least was born when Venus first appeared at Wimbledon, unlike 53 players in the women's draw, won four games in a row and took the opening set despite a fierce struggle to hold serve at 5-4.
Williams had more treatment before the start of set two but dropped serve immediately with a forehand into the net.
The crowd offered plenty of vocal encouragement, one fan shouting "You've still got it Venus" as she fought to extend the 355th Grand Slam singles match of her career - a total surpassed only by her sister Serena (423).
But former world number three Svitolina, who enjoyed a fairytale comeback from maternity leave by reaching the French Open quarter-finals last month, was ultimately just too sharp as she moved into a 5-1 lead.
Williams, who also won the title in 2000, 2001, 2005 and 2007, went down swinging, unleashing some thunderous strokes to claw back two games and hint at a fightback.
Svitolina got the job done though and as the evening sunshine turned to shade, Williams walked off beaten, waving what might have been a final farewell to the crowd.
Asked if she had considered pulling out after her slip, Williams said her only thought had been trying to figure out a way to win. "Try to fight to live another day," she said.
