Best has been instrumental in helping Ulster finish the regular RaboDirect PRO12 season top of the table and he responded to the news by turning in a fine performance against Cardiff Blues last time out.
And Anscombe is convinced Best was worthy of joining Ulster teammate Tommy Bowe on the trip to Australia.
"Everyone was hurting for Rory when the team was named and it was tough on Tommy [Bowe] because you want to celebrate with one but the other one was hurting, so that was tough," he told the Irish Independent.
"But true to the professional he is, Rory bounced back and he came to training next day and he was energetic and vibrant and looking forward to the game and wanted us to do well and finish the season off on a high.
"He should have been in the team. It is as simple as that, as far as I'm concerned.
"Sometimes when you see teams like this selected you need someone in the room pushing your case and, unfortunately, he didn't have that.
"That's unfortunate for Rory, but we know that he is a tough, quality player and he showed that the way he came out and fronted up against Cardiff."
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