Klaasen said they hope to go to another level in 2019.
"When we started our year last year we were a different position," said Klaasen. "We were trying to figure each other out, to see what we could do and as the year progressed we got better.
"[We are] starting out this year a lot more in sync and hopefully we can build on that. Always want to keep improving and look to get more out of yourselves."
Venus and Klaasen were a class above for much of the match, with Venus a standout on serve while Klaasen's movement and touch impressed.
"It was solid," said Venus. "We came through the tight points, we won a lot of the close points.
"There are still some things we can touch up on, so we will get back out on the court and back to work tomorrow."
Earlier Venus was an interested spectator from the players balcony as Statham completed his upset victory, becoming just the second Kiwi this decade to beat an overseas opponent at the Auckland ATP event.
"It's huge," said Venus. "A massive win. I don't know the last New Zealander to beat someone inside the top 30 but it has been quite a while. Hope he uses it as a bounce and keeps moving up the ranking this year."
Venus and Klaasen face Joao Sousa and Guido Pella in the quarterfinals on Thursday, Kiwi Marcus Daniell and Wesley Koolhof (Holland) are in first round action tomorrow against Pablo Cuevas and Leonardo Mayer.