Williams lost 6-1, 6-3 to the 79th-ranked Russian in what was the 32-year-old's first opening round loss at the All England Club since her 1997 debut.
But the former world number one -- the champion in 2000, 2001, 2005, 2007 and 2008 -- believes she can still compete at the top level despite her ranking having slipped to 58 after a six-month absence fighting serious illness.
"There's no way I will give up just because I have had a hard time in the first four or five friggin' tournaments back. That's not me," said a fiesty Williams at a post-match news conference.
When asked if she will play at Wimbledon in 2013, she was adamant.
"Sure," she said. "I feel like I am a great player who has had to deal with exceptional circumstances.
"I don't have time to feel negative. It doesn't feel good. I am as tough as nails, I don't have time to be sorry for myself.
"I can keep going for a while. You will see me playing here again next year."
The American star arrived at Wimbledon, where she was unseeded for the first time since her 1997 debut, short of confidence having been sidelined with Sjogern's Syndrome, a disease which causes joint pain and fatigue.
Monday's defeat was just her fourth loss at the first round stage of a Grand Slam against 52 wins.
After pulling out of the 2011 US Open, she only returned at Miami in March when her ranking was 134.
That presented her with an immediate problem -- her ranking was too low to gain a place at the Olympics.
"I am proud of the efforts I made to get my ranking back up in time for the Olympics," she said.
"That was one of the toughest things I have ever done in my life. I came back early, but I can't say if I am paying for that now."
Since her return, Williams has reached three quarter-finals -- Miami, Charleston and Rome.
But she was a second round loser at the French Open where the impact of her efforts began to tell.
"I have lost before and I know how to deal with it," said Williams after Monday's 75-minute defeat out on Court Two.
"I came in with a positive attitude and wanted to do my best. Life is challenging but I am up for a challenge."
Vesnina, who had lost in the first round of nine of her last 10 Grand Slam appearances, will face Polish third seed Agnieszka Radwanska for a place in the last 32.
(For more sports news and updates, follow Ahram Online Sports on Twitter: @AO Sports / and facebook AhramOnlineSports).