"I don't think we are favourites for fourth place," ESPN quotes Howard as saying.
"It is a little bit in our hands as we have a game in hand and we go head-to-head with Arsenal, but they still have four points on us and it is difficult. So we are on the outside looking in - but I think you want to be in the fight always.
"Sure, Arsenal are still favourites for fourth; they are four points ahead of us - but it's our job to make those four points up. If we can do it, then I suppose we will be favourites."
Everton were beaten 4-1 by the Gunners when the teams met in the FA Cup quarter-finals last month.