Three successive draws in the Premier League have left the Reds in the bottom half of the table.
But Johnson claims coming from behind to earn a share of the points against Chelsea at Stamford Bridge on Sunday proves how much the Reds are improving under Rodgers.
"If we had been offered a point before the game we probably would have taken it," said the England full-back. "Playing away at Stamford Bridge, it was always going to be difficult. Chelsea are very strong at home and we were expecting a tough game.
"We didn't start well, they got the goal and, usually, when Chelsea go in front here, they win.
"A lot of teams would have rolled over and ended up getting destroyed by four or five. But we have a great spirit in the dressing room and a lot of heart.
"We always fight to the death. We did that and got our reward.
"They had a tough game in Europe in the week and I think that showed in the last 15 minutes as Chelsea tired a little bit.
"We were strong, and in the closing stages, we really drove at them. We could have got all three points in the end but, overall, I think we've got to be happy with the draw."