Byron Moore equalised for the vistors after Lee Cook fired Orient, who had already hit the woodwork twice, into the lead.
"I thought that we competed well and I was pleased with the draw at the end," said Davis.
"I thought it was a decent game. It's a tough place to come to, we never seem to get a lot when we come down south but we've got a point and I'm happy with that.
"We did better once we scored the equaliser. Up until then, it had been a case of staying in the game to be honest.
"We had got lucky with them hitting the post twice and we could have been two or three down. They came very strongly at us at the start of the game and we certainly rode our luck in that period.
"But once we back on level terms, we then started to get back in the game and we showed a lot more confidence and grew into the game.
"We've been encouraging Byron Moore to get in a that back post many, many times, he had only done it once before
and scored and now he's done it again, so maybe it might finally twig that he's got to get in at that back post!"