The Sweden international insists the Black Cats have learned from their 4-0 defeat at the Hawthorns two weeks ago after drawing with Newcastle and beating Liverpool
The Black Cats had been on a fine run of form following the arrival of Martin O'Neill as manager but suffered a shock 4-0 defeat at the Hawthorns a fortnight ago.
But having after a draw against rivals Newcastle and a win against Liverpool at the Stadium of Light on Saturday, the Swede says Sunderland have learned from their mistakes against the Baggies.
"We know what we have to do to be successful. Since the manager came in, we have had one reality check and that was away to West Brom," he told Sky Sports.
"We said then, 'Let's not repeat that', and so far, we haven't. If we work as hard as we did today and last weekend, we know we are a good team.
"We know we can win games and we have beaten some big teams here now, and we feel very close to them."
Lee Cattermole, Stephane Sessegnon and Kieran Richardson were all unavailable for the win over Liverpool, which was secured thanks to a second-half Nicklas Bendtner goal.
Larsson added: "It's obviously disappointing missing them, they are three very good players and they have done very well for us.
"But the manager said before the game, 'Let's not worry about that, let's focus on whoever can play and what we can do'.
"We were desperate to get the three points today and we are more than happy that we got them."
Sunderland now lie eighth in the Premier League and two points behind Liverpool, who have a game in hand, following Saturday's result.