West Ham sit in the bottom three and have just axed manager Graham Potter and replaced him with Nuno Espirito Santo.
Kilman told the club's website: “We’ve not started off the season how we wanted.
“As a group, we have much bigger aspirations within the team, and we obviously need to try and find a way to get back on track, but it's really early in the season, and it's a time where we need to stick together, stay positive and continue to give everything we’ve got, and we believe we can turn things around.
“I think it's just the little fine details. For 95 per cent of the games, we've been dominant, and we've been good, even against Tottenham, a team that's really strong. It's just the fine margins that really cost us and have really killed us in crucial moments in the game, and we need to try and find a way to nullify that.
“It just takes one or two good results, and then you're back on track to where you want to be, and we can build from there. Everyone’s working hard, but we just need to cut out the little fine margins in games, and hopefully, we can kick on for the rest of the season.
“We've got a really experienced group of players. We’ve got players who have played so many Premier League games and have been in situations like this before.
“The Premier League is the hardest league in the world, but I think we've got a good group in here that know how to handle these situations and know how to come out the better side of it.”
Nuno's first game in charge of West Ham will be on Monday night against Everton.