Brentford remain unbeaten so far this season, with one win and two draws from their opening three Premier League games.
Vitaly Janelt opened the scoring just after half time, but Sunderland ensured the spoils were shared through an Enzo Le Fee penalty.
Speaking to BBC Match of the Day after the game, Andrews admitted that his side’s own mistakes cost them the win.
"We caused ourselves a lot of problems. We were better in the second half. We started fighting more, did the ugly side of the game and played with a bit more conviction," he said.
“There was a real improvement and I thought the game was there for the taking in the second half.
"The fact we're looking round the place and there is a tinge of disappointment. Nothing is given to you in this league - you have to go and earn it."
On Sunderland's penalty: "I need to be a bit careful. Overall I didn't love the decisions today. In terms of the penalty, I don't have too many qualms about it."