"It was s a tough game; of course, it's hard to lose that matchup," Kontaveit said after the game, ERR's sports portal reports.

"Overall, it wasn't a bad game, it was just another match after a long injury break. Naturally it's hard to get close, but I think I fought well and it was such a knife-edge game. My opponent was very strong; the conditions were better for her," she added.

After winning the second set 6:2, tying things up in sets, the decider saw th scoreline in games remained very even, ending up at 5:5 at one point. However, Bertens won the next game, and found herself with two matchpoints in the one after. Although Kontaveit staved off the first, the second was a bridge too far and Bertens went through.

Bertens faces world number three Naomi Osaka (Japan) next.

"At important moments, of course, I would have liked not to get lost, but that's how it went, tennis is like that," the Estonian, 24, from Tallinn, added. 

"A very tough, tough top league fight against a top ten player - I think nothing went wrong; I definitely didn't play badly," Kontaveit, who only recently bounced back from an illness which cut short last season during the U.S. Open in October, said.

The tournament was part of a season-starting warm-up set of competitions, ahead of the Australian Open at Melbourne Park starting on January 20.

Kontaveit is in action next week at the Adelaide International Tennis Tournament.

The competition went ahead despite the widespread bush fires in Australia, including some burning close to Brisbane. Australian players including world men's number two Nick Kyrgios have helped to raise money towards the relief efforts.