Last year's Six Nations Grand Slam winner was stunned by England in its Dublin opener, but bounced back with a 22-13 triumph at Murrayfield.
While Best was still not entirely content with the performance level, he reiterated his belief in the rallying visitors.
"We have a lot of belief in what we're doing and how good a team we are," Best said. "That was a really tough game, it was tough mentally in the build-up to it.
"We asked for a reaction, we asked for a physical reaction that we probably didn't get last week and I think we got that.
"It wasn't the most spectacular game of rugby there ever was, but I think it was two teams going hard at each other and we are very, very grateful to win.
"We had our chances and we took them, we were clinical. We've obviously got a lot of improving to do but, at the same time, we just had to wear them down.
"They were well organised in defence and we knew how dangerous they would be in attack. By and large we fronted up to the task, as we had to."