Liam Ridehalgh's first goal for Rovers four minutes before half-time cancelled out Sam Baldock's 14th-minute opener, extending both sides' unbeaten run to five games.
Moore's men remain in the relegation zone though, and he believes their home from could prove the key to them getting out of trouble.
"We need to win our home games and it would be nice to get out of the bottom four because it is really tight down there," said Moore.
"It was a massive game for us and we really needed to win it but we just didn't produce it before the break.
"We didn't start so well and we gave away a sloppy goal but overall I am disappointed not to have got three points.
"Bristol City were probably the better side in the first-half but in the second half we came out and had a real good go at them.
"We got in some great areas but the final ball just wasn't there.
"If we had started the match like we did the second half then we would have won the game.
"We kept plugging away but I just felt we were waiting for something to happen inside the box and we needed to be hungrier for goals."