The 2-1 loss at Elland Road marks the worst start to a season for West Ham for 52 years.
The Hammers now sit 19th on the Premier League table and Bowen said: "Not good enough. We started well against Brentford the other day and wanted to do the same, but the way we defended the goal was really poor. We wanted to get back into it. From a corner again, it's not brave enough. It always felt like one goal could get a bit of confidence. We did that, but it's too late.
"Probably a lot of reasons why. But a dressing room when you're second bottom of the league is low. The only way this will change is if we step up and show some fight. We need more of that. It's easy to hide and be scared almost. It's easier said and harder to do sometimes. Roll your sleeves up and dig in. No one will give this to us. We're in a real situation and we have to face the reality of that. You have to face up to the reality of where we are and we're in trouble now.
"We have to go out there and fight more than anything. The Premier League is the hardest league. We're not playing well and not getting results. We need to change it. We're the only ones that can change it.
"We've talked as a group, but it's down to the players as well. We speak to each other, but there's only so much. It's got to come from within. We can show it a lot more. Nine games we've had, one win and we're second bottom. We haven't been great at home, but now is the time to roll your sleeves up."