Serena Williams won in straight sets again and tied a major record, yet the world number one was not satisfied with her performance in the US Open second round.

Williams advanced with ease after seeing off fellow American Vania King 6-3 6-3 in New York on Thursday.

The 34-year-old wrapped up proceedings in 64 minutes at Arthur Ashe Stadium, but she was less than satisfied with her display, having tallied 28 unforced errors compared to King's 11.

"I just think it should have been a different scoreline for me. I feel like I made a lot of errors," said Williams, as she looks ahead to a meeting with Johanna Larsson.

"But there's nothing I can do about that now. What really matters is I got the win. Hopefully I'll just get better.

"I just didn't have a great day today. But it's always good to get a win when you're not – I definitely don't think I played the way I did in my first round [a 6-3 6-3 win over Ekaterina Makarova]. But it's all right."

With the second-round win at Flushing Meadows, Williams matched Martina Navratilova's professional-era record of 306 grand slam match victories.

Asked about the feat, the 22-time major winner said: "I knew it was on the horizon. I knew at Wimbledon that I wanted to get there. Obviously I'm excited about that. Would like to take one more step, several more steps.

"Sometimes I don't even know that I'm hitting these milestones. But some of them I'm really proud of. Like this one's kind of cool, to win 306. That's really a cool milestone."