Despite lying 11th in the Premier League table, Hull remain just five points above the drop-zone after only one win in their last nine league games.
The Tigers have been in tremendous form at the KC Stadium this season with the sixth best home record in the Premier League, better than Manchester United, but only five of their 23 points have come on their travels.
City have away games coming up against teams around them after their tough start to the season on the road and Bruce is aware these will be the games that will eventually decide their fate.
"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," Bruce told the club's official website.
"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."