Sullivan believes that building on the 2-1 victory over Manchester City and picking up wins at home will be key for the Hammers.
The West Ham co-owner has also admitted that the team were lucky to win against the Citizens at the Etihad Stadium in the Premier League on Saturday evening.
“We must accept that we played the best team in the league this season and rode our luck a bit,” Sullivan wrote on West Ham’s official website. “Our wins over Liverpool and Arsenal were decisive, but this was a very marginal victory.
“The key is now to build on this and improve our home form. That said and done, we fear nobody and know we are capable of beating anybody. This could be a very special season.”
The win against City at the Etihad was West Ham’s third in a row on the road, with Slaven Bilic’s side having defeated Arsenal and Liverpool at the Emirates Stadium and Anfield respectively already this season.
The Hammers are now third the Premier League table with 12 points from six matches, just three points behind leaders City.
A top-four finish is probably not within reach for the London outfit, but the way they are playing at the moment suggests that they can end up in the Europa League positions.
It’s early days and Bilic’s team need to start winning home matches, but the signs are very promising for the London outfit.