The Baggies remain rooted to the foot of the Premier League table at present, three points from safety.
They have taken just one point from their last four fixtures and are running out of time in their efforts to secure their top-flight status, with only 12 games remaining this term.
Mowbray, though, continues to look on the positive side, believing he has seen enough from his players in recent weeks to suggest they are ready for the challenge.
"I don't think confidence has taken a knock," he told the Birmingham Mail.
"I think in the media world it is easy for people to suggest that. We got beat by Fulham (2-0 on Sunday) who have beaten seven other teams at home this season. It is not as if they are mugs.
Tough games"I think sometimes the perception is 'oh it's Fulham' and we should get something there. If it had been a Fulham side that hadn't won a game all season then I think everyone would be in their right to ask questions but Fulham have beaten better teams than ourselves at home. We just move on to the next game.
"Has the confidence taken a knock? I think after any defeat you can get down about it but you have to bounce back and get ready for the next game, which this week is at Everton and it is another tough fixture.
"They have been going well and riding high in the league, but they are all tough games so we will go there and try and make life as uncomfortable as we can for them, and try to cut out the individual errors that are costing us.
"Let's see if we can get our noses in front and see if we have the capabilities to see a game out. We did it earlier in the season at Middlesbrough and that is the sort of resilience we are going to need to show in one of these games, because I feel we do need to find a win away from home and then win the games at home we need to win.
"If we can do that, I am pretty sure we will be fine, but we need to keep going and stick together, and I think the boys are fine."