The Premier League basement side have just one win on the road this term and Mowbray knows that is not good enough.
Albion travel to Fulham this weekend and Mowbray is hopeful they can grab their second away success at Craven Cottage.
"We haven't had the points return our away performances deserve. We have had some bad days, like Sunderland away, but generally we have deserved more," said the Baggies chief.
"Now we are coming to a stage of the season where we have to start proving that.
"We have two opportunities in the next couple of weeks to get our next victory away from home.
"I am pretty sure it will come and I am very hopeful we won't go through this season with only one away win under our belts. Our performances have warranted more than that.
"Let's hope we can do what teams like Wigan and Fulham have and go on a run where you win three or four games on the bounce.
"I think we are more than capable of doing that and then you catapult yourself out of trouble."