The Toffees have moved up to seventh and within four points of their arch-rivals in the Barclays Premier League after a five-game unbeaten run. Everton have finished above their neighbours just once since last winning the title in 1987 but Howard believes momentum is on their side and is anticipating an exciting Merseyside battle over the remaining seven games.
The 32-year-old American said: "We have still got miles to go and we want to keep cracking on. Our natural-born rivals are right ahead of us and we are going to try to nip on their heels and get a couple of results."
He added: "The rivalry is amazing and for the city this run-in will be great. We are going to try to overtake them and I am sure they are going to try to do everything to crack on in the table as well."
Everton have spent most of the season in the bottom half of the table and were just three points above the relegation zone at the end of February.
Howard added: "We have under-achieved, and that falls squarely on the shoulders of the players. But we have done enough to dig in and get ourselves into seventh position.
"We have an opportunity to look forward and get some more results and push even higher. If you'd have said that to us around Christmas we would have snatched your hand off."
Everton are set for a testing run-in as they face a series of teams, starting with Saturday's trip to struggling Wolves, with either relegation or European issues to play for.
Blackburn, Wigan and West Brom have all been involved in the fight for survival while Manchester United, Manchester City and Chelsea are in the top four.
Howard said: "That is what makes England beautiful and the Premier League amazing. There are cup finals everywhere you look. No team can just cruise with six or seven games left. It is impossible to do that."
Source: PA
Source: PA