The Toffees have secured a place in the Europa League for the first time in five years after finishing fifth in the Premier League last term.
Howard believes that the competition offers the club the best opportunity to win their first piece of silverware since lifting the FA Cup in 1995.
"When I first came here nine years ago, it seemed like almost every year we were in Europe and it's good to be back there," he told Sky Sports News.
"Those evening games under the lights will be good for our fans and I don't kid you when I say we are going to try and lift a cup this season.
"We don't care whether that's in Europe, the FA Cup or whatever - and we're going to try and go well in the league. We have the squad and the talent. We know there will be some tough nights but we will enjoy it."
Everton face German side Wolfsburg at Goodison Park on Thursday night.