"No matter what people think of what we're doing, we need the crowd with us," said Southgate after Saturday's 1-1 draw with Tottenham.
Southgate, whose side are just three points off the bottom, added: "I think the supporters are frustrated and they showed that with their reaction at certain times.
"Expectations are very high at any club in the Premier League and people don't have the patience to wait for things to turn around."
"You accept that any decision you make when you are in the position you are in is going to be queried and highlighted.
"That's part and parcel of being a Premier League manager so if you don't like it, or you're not prepared to put up with it, don't bother."