Despite sitting 11th in the table, Hull boast the joint-worst away record in England's top flight, having picked up just five points from 11 games.
Bruce pointed out that many of his side's away games to date have involved visits to top-10 sides, but admits the Tigers' form on the road must improve if they are to stay in the Premier League.
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"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."
Bruce is also hoping to witness a greater attacking threat from Hull following the recent arrivals of Nikica Jelavic and Shane Long.
"We pride ourselves on our defensive organisation, but we can't keep relying on our defenders to keep a clean sheet every week," he added.
"We have to pose a threat at the other end and have the belief to take the ball on and play better. Norwich was a harsh lesson in that. We made a mistake and the game was past us."