The Cottagers were level at the break, but a second-half collapse saw the Saints cruise to a comfortable win.
"We are in a situation where we seem to have to drag the ball over the line. Artur Boruc made some great saves. It was the same against Swansea. We should have taken the lead but we didn't," manager Meulensteen told BBC Sport.
"The second goal really killed us. We have to work hard and keep lifting ourselves. It (going bottom) was always a possibility.
"Now we have to stand up for ourselves. At least we have some new faces in and guys who can breathe a bit of confidence into the group."
Fulham are three points from safety.