Why Liverpool are still a work in progress under Jurgen Klopp
Jurgen Klopp is rightly getting plaudits for the feel-good factor he has generated at Liverpool, but if you judge him on his choice of central defenders then he is far less convincing.
The Reds manager made a lot of changes over the summer in what is a specialist position, which is fair enough when you think about the issues his side had there last season.
Unfortunately for Klopp, from what I have seen, the players he has brought in at the back are not better than the ones who have left.
Klopp has also got problems in midfield and attack to deal with before Saturday's Premier League trip to Tottenham - and Liverpool having to play their first three league games away from home hardly helps matters.
Klavan is going to have to improve - and quickly
Klopp let two of his centre-halves, Martin Skrtel and Kolo Toure, leave over the summer so I was expecting his most experienced new signing at the back, Ragnar Klavan, to be a world-beater.
So far, the 30-year-old Estonian does not seem to be at the same level as Skrtel or Toure, let alone an improvement. If he is going to stay in Liverpool's defence for the rest of the season, he is going to have to get better quickly.
He was beaten twice for Burnley's second goal, once by Steven Defour, who ran straight through him, and then by Andre Gray, who went round him as he tried to recover.
Klavan was involved in the Clarets' first goal too. Nathaniel Clyne gave it away for Gray to set up Sam Vokes to score, but Klavan had put his team-mate under pressure by trying to play out from the back with a long cross-field pass that saw Clyne closed down as soon as it reached him.
On that evidence, a change in personnel has not seen the defensive problems that held Liverpool back last season go away.
Man-management of Moreno has left rebuilding work to do
We currently have the best group of managers in the Premier League that I can remember, and Klopp is clearly one of them.
In many ways his approach has been a breath of fresh air but that does not mean he gets everything right, even in areas that I regard as among his strengths.
Klopp is a manager who improves his players, partly by boosting their self-esteem, and I thought that was what he was doing when he defended and protected Alberto Moreno following criticism last week.
It was great to hear a manager say 'look, he was not perfect but we can work on that and make it better' - yet he then pulled the plug on Moreno and played James Milner at left-back against Burnley instead.
That left me thinking that maybe Klopp is saying one thing to the media and another to his players.
I don't think the solution was to play Milner there and now he has dented Moreno's confidence too.
If he is going to ask Moreno to come back this weekend against Tottenham, he has some rebuilding work to do.
Sitting role does not suit Henderson
The other thing Klopp has to do before the trip to White Hart Lane is work out a way of protecting his defence better than at Turf Moor.
He went with a very attacking line-up against Burnley and, when you go out with the intention of pressing your opponents high up the pitch, you leave your back four more exposed.
That high-pressing game needs to be adjusted when Liverpool are playing against a team like Burnley that play direct football and are only looking to counter-attack with pace. In those circumstances, Liverpool must show more control.
I would also question whether Jordan Henderson is the ideal player to be sitting in front of the defence in their 4-3-3 formation.
For starters, he does not want to sit and a big part of his game is about getting up and down the pitch.
Also, because of the way Liverpool try to work the ball forward, that role means he sees more of the ball than anyone else because play comes through him and he has the responsibility to launch a lot of attacks.
That does not suit him either. I am not sure Henderson has the range of passing to hurt the opposition. He certainly did not do it against Burnley.
We still don't know which Liverpool will turn up
I was watching Klopp's reactions during the game at Turf Moor while I was on Final Score last Saturday and I thought he kept remarkably restrained considering what he was watching.
It is early days but, after two games of the new Premier League campaign, his side still seem to be where they were last season - you do not know which Liverpool are going to turn up.
They need to find a better balance and on Saturday they will face a Tottenham team that have exactly that.
Under Mauricio Pochettino, Tottenham are well drilled and, even if they do not click going forward, they do not give much away at the back.
You would not say that about Liverpool at present. It seemed to me that they lost the game at Burnley by trying to win it, and they have to learn from that.
The power of a positive atmosphere
Liverpool remain a work in progress but some of the problems I have mentioned could be solved by players already at the club.
Another of their new centre-backs, Joel Matip, is back to full fitness and Emre Can could be the answer in the centre of midfield, with Henderson using his energy in a wider position.
One thing they definitely have in their favour is how proud the Liverpool fans are of Klopp and what he has brought to their club.
We have seen the best and worst of his Liverpool team in the last couple of weeks but everyone still trusts in him, and he realises how powerful such a positive atmosphere can be.
Martin Keown was speaking to BBC Sport's Chris Bevan.