The Cherries began their Premier League campaign with a 1-0 defeat against West Brom, as the team had a lot of ball possession but very view scoring opportunities.
"You have got to be so careful not to think you've just cracked it. You can't relax and think, we've had two seasons here now so we're alright", the 30-year-old midfielder said.
Bournemouth will face Watford on Saturday, and Surman was really impressed by them during their 3-3 draw against Liverpool.
"Watford looked very strong on Saturday. Although they salvaged a point at the end, in a way they probably did enough to win the game", he said.
Bournemouth signed Jermaine Defoe in the summer as well as Chelsea's Nathan Ake, and Surman is heaped praise on Defoe.
"Jermain is calm, collected and I think that's massive, especially when things aren't going that well. And even when they are, he is experienced enough to keep people's feet on the ground", he added.