"That's the beauty of sport, it's unpredictable," said Budge.
"You want players to turn up who want to win and I think you saw two players tonight who desperately wanted to win matches."
Budge joked Wozniacki was now feeling the pressure.
"We had a bit of a text exchange tonight actually. After Venus' match she sent me a text and said 'it almost could have been two'. [Wozniacki] didn't play as well as she hoped today herself."
"But that's the quality of this tournament, anyone of those girls coming through can win this tournament, and we're lucky we still have some real quality in Wozniacki, [Svetlana] Kuznetsova, [Sloane] Stephens - there's some exciting talent in that draw."
Williams has promised to stick around in Auckland for a few more days yet and said she's happy to put herself to work with sponsorship commitments and public appearances - an offer Budge has gladly accepted.
"I think she's the greatest sportsperson that has come to New Zealand for a very long time and we owe her a great deal of gratitude, so anything Venus wants to do in Auckland over the next few days we'll make sure it happens," said Budge.
Williams looked out of sorts throughout the match, while Kasatkina produced the performance of her life.
And although it's normal for players to suffer from early-season rust, the top seed just couldn't get going against the world No 75.
She accumulated 73 unforced errors, making it impossible to win any game, let alone against someone who was returning everything with interest.
"She is an amazing tennis player and I respect her so much," said a stunned Kasatkina. "It was an unbelievable match for me."
Tennis fans were not impressed with the top seeds' performances, with many taking to the ASB Classic Facebook page to register their disappointment.
One, Rick Delasau, wrote: "The ASB Classic is on life support now... very sad. The whole tournament has lost its spark now... who knows if we ever see the likes of these women again? I'm holidaying in NZ at the moment, visiting family, and am really devastated. I looked at the potential quarter-final match-ups and instead of being excited, I might be [heading] for a long lunch down at the pub."
Another, Nath Gain, wrote: "Totally sux for the tournament. Rather ridiculous that the top 2 seeds get knocked out in the first round! Not too good for ticket sales. The other players played some really good tennis, but they both looked really out of form!"
Corey Nicholas posted: "Gutted. If you've got tickets for tomorrow or Thursday hahaha."
