The Tigers lie 11th in the table but have relied on their impressive home displays for that position, picking up just five of their 23 points on the road.
Their next three away trips - to Crystal Palace, Sunderland and Cardiff - are all winnable matches and Bruce knows they must beging getting results in those matches.
"I've said repeatedly that we've already been away to all of the top nine, apart from Manchester United, and so it has been a particularly difficult start in that respect," he said.
"But we have to make sure that when we go away from home from now on, we have that mentality that we've shown in our home games.
"Unfortunately, we haven't shown that away from home as yet. We're new to the Premier League and we have to find a way of picking some points up away from home.
"It's so tight and you can throw a blanket over everybody in the bottom ten. It's going to be about an accumulation of points and you need to get to that 38-40 point mark."