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.
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 to BBC Sport.
“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."