The Hammers are currently in 11th place in the Premier League table following two defeats and one win from their opening three games.
Despite struggling for points so far this term, Poyet believes that West Ham are good enough to enjoy a successful campaign.
"So far the first team results haven't being going our way but I don't think we are far away from turning the results around," the former England youth international told the club's official website.
"I think we just need to keep going. We've got a lot of new players coming in and several people coming back from injury as well. We've got a really good squad for this year. If we are all fit, I think we could do really well this season."
West Ham return to action next Monday when they travel to Hull City in the league.