Liverpool conceded again from another West Brom corner in the second half, before substitute Divock Origi salvaged a point with an injury-time equaliser aided by a deflection.
Klopp was asked his opinion on Mignolet's performance after the game, but refused to blame the Belgian for the mistake.
"I said to Simon at half-time: 'If somebody says it was your fault, you can say it's not true, it's my fault' -- because I want a keeper who helps, a keeper who comes out and tries everything," the manager was quoted as saying by the club's website (www.liverpoolfc.com).
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"In this there were 20 players around him. He tried and didn't get the ball for the first goal.
"The next one I have to see again. It was at the near post, which is usually not the goalkeeper's responsibility, we have people there who have to make a header and defend this.
"But there's nothing negative to say about Simon. For the first goal he tried and that, for me, is important.
"I want the goalkeeper to come out because he can help. Sometimes you try something and make a fault -- it's not the biggest problem, you go on."
The draw left Liverpool ninth in the Premier League table on 24 points and without a win in their last three games in all competitions.
(Reporting by Simon Jennings in Bengaluru; editing by Sudipto Ganguly)
