With the Toffees passing Arsene Wenger's faltering Gunners for fourth place, the American goalkeeper says there is a "good energy" in the locker room.
Saturday's 1-0 win over Sunderland saw Roberto Martinez's men claim their seventh league win in a row as the club leapfrogged Arsenal into the fourth spot for the first time since January.
"The manager drilled into us that it would be tough," he told the Liverpool Echo. "Now we can count them on one hand. We're going to tick the games off.
"We're in a good mental state. We're performing well. We feel fluid and there's a good energy in the dressing room. We won't feel pressure on our back from Arsenal.
"Anything can happen. There are so many 'ifs' and 'buts' but if we keep fighting we'll finish strong so hopefully that can continue. We wanted it in our own hands. We worked so hard to get to this point that we don't want to throw it away now.
"It couldn’t be better than that. As much as you keep fighting if you’re having to hope that Arsenal lose, that's draining. To be able to just focus on us is helpful."
Everton was made to work for the three points Saturday, with Wes Brown's own goal 15 minutes from time deciding the match.
But Howard feels the resilience shown by the Toffees at the Stadium of Light is further proof of their determination to finish the season as strongly as possible.
He continued: "You don't mind it being a bit scrappy every now and then because you almost want the confirmation that we've got it in us.
"We know we can play good football but we never want to get away from that Everton fighting spirit, that ability to dig in. Games like this remind us that's still in us, which is important. Even at 1-0 down they kept coming because they had a lot to fight for and it was a really tough game."