Two draws for the champions in the last week have given leaders Manchester United a nine-point cushion with just 13 matches left.
And keeper Hart admits they cannot afford to let their neighbours - who host Everton 24 hours later - disappear any further over the horizon.
He said: "We have to win at Southampton. We can't hide the facts - we are nine points behind with 13 games to go, so we need the win.
"We need to do what we did in the last seven games before Sunday, when we won six and drew one.
"But, of course, we have now drawn again and it is not enough. We need to start winning.
"We will always be in it but unfortunately it's a big gap - getting too big for our liking. You have to move forward and that means we have to beat Southampton."