Liverpool won the League Cup and reached the FA Cup final under Kenny Dalglish last term, but registered a joint lowest Premier League finish of eighth.
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"Brendan was brought in to rebuild the squad and put Liverpool back into the places that it should be," Johnson told reporters.
"He wants to put us back in the top four, but he wasn’t asked to do that in his first season. This season has been a step closer to that.
"Of course everyone - players, staff, fans - would love us to be back in the top four, but if we improve on last season, then it is a step in the right direction.
"You look at the squad we have, the feeling that there is around the place, the football that we are playing and, eight times out of ten, we have been battering teams.
"That wasn’t the case last season. 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."