The team lack of quality since the season started, this won't change overnight with change of manager.

Allen + Benteke failed to score in 1 v 1 situation simply highlight further the lack of quality in front of goal.
Benteke has chance to restore the 2 goal margin lead with 1 v 1 situation, yet fail to hit the target again.

Soton players just gave Liv's players a lesson how to shoot properly.

Defence was symbolic especially after Skrtel came in.

Klopp got it wrong last night, Hendo should come in after about 50-60 min to protect the lead, especially with the penalty conceded time, which already tell tale sign very wrong of the team after starting the second half, with Soton substitution.

Second half remind us the Klopp still has a lot of work to do to sort out the defence which had been leaking goals easily for the last 3 years.

The team has been like that for the past 3 season, may be lack of proper defensive coaching for too long time already that deep rooted in players mind.

The main problem for this team,

1. Scoring goals, sometimes should just shoot instead of pass, and nobody apart from Sturridge and Coutinho have a shooting boot. If both of them didn't score, nobody else.
Midfielders hardly score many for the entire season, CB also lack of goals through set piece/corner through header.

There were plenty of chance created in the first half against Soton, as well as match against MU in Europa league first leg, but failed to score many, aka conversion rate is still one of lowest in the league.

2. Can't defend proper and professionally see out the game.

Ya.
Firmino turns into different player under Klopp.
He was also goal shy before Klopp came in.

You need to have fair share of midfielders' goals, as well as CB/LB goals especially during set piece or corner time.
If only 2 striker/front man can score goal, it is very easy for opponent to defence upon.
Hendo, Can need to score more goals.

Moreno is not a good winger, a good winger provide lot of assist and good crosses to striker whereby we seldom see this.

He strength is burst of speed from the back, and overlapping, whereby it can make opposition defender need to chaseback/shadow, but when reaching opponent penalty box, become like clueless and little contribution to actual goal threat already.

In term of defensive wise, positioning, ball watching always a questionable issue.

Nowadays, it become rare for team to use 4-4-2, with traditional winger system already.
Most LM,RM tend to cut in to middle one or pseudo CM.

And a lot of managers opt for single striker system, either 4-2-3-1, 4-4-1-1, whereby winger to supply cross to 2 striker upfront from byline become rare to see.
Fullback is the one provide the width nowadays.

I find funny to hear that a striker who had problem to score goal, even with multiple 1 v 1 situation, made a complaint that the club manager did not want to play him.

Starting position or play time is earned, not automatically given.