David Moyes' men have been left with nothing to show from their meetings with Manchester City and Liverpool, with the latter defeat overshadowed by Jack Rodwell's now-rescinded red card.
The odds will be against the Merseyside outfit taking anything from their trip to Stamford Bridge, but America international Howard believes the weekend clash will bring the best out of the visitors.
"We enjoy battling against the odds and proving people wrong. If there are doubters out there, it's good to go out there and get on a run of form," he told the Liverpool Echo.
"We don't have to go out and spend ?100m, we know we can still go out and compete with the quality we have. It's not always easy but we've shown that.
"We've got a great fighting spirit. We love to fight for the shirt and each other. We've got a grit and a determination about us that is hard to match and the top teams don't enjoy playing Everton.
"The one thing we've also always had is bringing through young players and we've got a fantastic manager, who's very shrewd in the transfer market."
Howard made his 150th consecutive Premier League appearance last month but knows he will have to remain on top form to keep recent arrival Marcus Hahnemann and fellow shot-stopper Jan Mucha on the sidelines.
"Marcus is fantastic, he's like a big teddy bear," Howard added.
"He's a good friend and a good guy around the training ground. His experience speaks for itself and he's a good goalkeeper. He'll be a good addition to the squad.
"I know he'll work hard every day, I need to be surrounded by top quality goalkeepers who won't let me let my guard down. If I can push myself to my limits, then the rest will take care of itself."
Source: Team Talk
Source: Team Talk