The Baggies have only won one game away from The Hawthorns so far this season - a 1-0 victory at Middlesbrough back on 27th September.
But Mowbray knows his rock-bottom side need to start picking up points on their travels if they are to avoid the drop, starting against Fulham on Sunday in a game being shown live on Sky Sports 1 at 1.30pm.
As well as the trip to Craven Cottage, the Baggies also play Everton and West Ham away in their next four matches, while they face the stern test of Arsenal at home in their other game.
He said: "With it being very tight at the bottom of the table we desperately need to pick up points and I honestly believe that there is an away win in the side.
"Looking at the remaining games there are matches I look upon as matches we can win.
Important spell"Obviously, we have a very important spell of games coming up against the likes of Everton, Arsenal and West Ham."
The Baggies lost their last match 3-2 at home to Newcastle and Mowbray hopes his side will bounce back from this major setback.
"Losing in the manner we did against Newcastle was a huge disappointment," admitted Mowbray.
"But I hope that we learnt from that defeat when we really handed the match to them on a plate."
Mowbray's side have spent the last week at a training camp in Spain and the Baggies boss believes the change of scenery has benefited his players.
He added: "Our trip to Spain was very good and it was interesting to see how the different players interacted.
Highly beneficial"We were able to work on different aspects of our game and there is no doubt it proved highly beneficial for everyone."
Sunday's opponents Fulham lost 3-0 to Man United in midweek but Mowbray is not underestimating the threat posed by the Cottagers.
He said: "You can see the quality that Fulham possess and that is the reason they are where they are in the table.
"Yet they conceded three goals against United and it could have been a lot more.
"I'm sure they are thinking West Brom are not as good as Manchester United and I heard a commentator say that Fulham rested a few players as their manager saw Sunday's match as bigger than the Manchester United game.
"I've been there myself several times this season where I've rested people as the game coming up behind is much more important."
The Baggies have been boosted by the return of on-loan Arsenal striker Jay Simpson, who will link up in attack with the on-loan Nancy marksman Marc-Antoine Fortune.
Mowbray hailed the pair's attacking prowess, saying: "I'm sure that if we had had the two strikers we've now got we would be in a much better position than we are at the moment."