The Liverpool manager is not happy his captain played 90 minutes on an artificial pitch.
The game that was a dead rubber as England had already qualified for the World Cup.
Henderson, 27, has been plagued by foot problems over the last two years.
The midfielder missed most of the second half of last season but returned to full fitness in the summer.
Liverpool face bitter rivals Manchester United tomorrow and Klopp was already not happy with the Premier League for the game being at 12.30pm following an international break.
But he was angered further by Southgate risking Henderson’s fitness with his injury history ahead of such a crucial game.
He said: “England played a friendly game on an artificial surface – it was a qualification game but they had already qualified – and I was not happy that Hendo was on the pitch to be honest with all the problems he's had in the past.
“It made no sense. We cannot be involved in this.
“They all make their own decisions. No manager of a national team asked me so far before a game 'How would you line up?'
Liverpool against United is always billed as one of the biggest games of the season and Klopp is bemused as to why it is so early after an international break.
He said: “Sometimes I would really wish we could have had more time to make preparations for such an important game. But is our job and the same for the other team. 'Let's go'.
“It’s a massive game, it’s great and I actually would really love to ask the Premier League to give us more time to prepare for a game like this.
“Our fans are waiting for two weeks at least, if not since last year but we have two days to prepare and it is the same for both clubs.”
