Rangers won their first game under Hart's management with a 2-1 success against The Robins at Loftus Road on Boxing Day.
"We hadn't won in six games and lost the lead in our last two, and there was an edginess in our game against a very good Bristol City side," Hart said after the match.
"We are fighting for any sort of rhythm but each player showed the right attitude to get a result.
"This club needed a win today."