The Reds have struggled over the past few seasons and although they sit seventh, and below Merseyside rivals Everton at present, full-back Johnson is confident of success under Rodgers.
"Brendan was brought in to rebuild the squad and put Liverpool back into the places that it should be," said the England international.
"This season has been a step closer to that. Eight times out of 10 we have dominated games. Sometimes, like against West Ham (in the 0-0 draw on the weekend), we haven't come away with the points that we deserve.
"We have battered teams but if we don't get that early goal, it has given them encouragement.
"Brendan wants to put us back in the top four but he wasn't asked to do that in his first season. If we improve on last season then it is a step in the right direction, and we have definitely done that.
"It's a few things. Look at the squad, the feeling there is around the place, the football we are playing.
"We won a trophy last season and of course that was fantastic. Everyone wants to win; that's what we are in the game for.
"But in terms of getting Liverpool back where they belong, we want to be back in the top four.
"I wouldn't say it has been a season when we have been so close but so far.
"It is clearly a better season than the last one. Brendan will look to improve again in the summer and if we can start nicking the goals we need from games like West Ham, we will be right in amongst it."