The Reds returned from the international break with a vital three points against their neighbours, with a late Mohamed Salah brace securing the victory in front of the Kop.
A second-half switch of shape saw Diaz operate as a left wing-back while Liverpool tried to force a breakthrough late into the game.
The manager explained the thinking behind the move after the match, revealing that the idea was for the Colombian to “attack” from a deeper area than he is typically used to.
“We brought on another offensive player and how you can do that without taking one off? You have to change a little bit. So we put Lucho in the left-back position,” the boss told TNT Sports.
“They didn’t have a winger really there, so we thought it was possible to let him attack there.
“And he crossed the ball for the penalty, so it was not the worst idea we ever had.”
It took 75 minutes to break the deadlock when Salah swept the ball beyond Jordan Pickford from 12 yards following Michael Keane’s handball.
The Reds needed to be patient against an Everton side that sat deep after Ashley Young’s dismissal shortly before the break, with Klopp admitting that he “would’ve loved” to have seen how the game panned out with a level playing field.
“Everton is not a team with that deep a block, so I would’ve loved to play the game 11v11 or 10v10 because it’s just a different game,” he continued.
“But with 10, they were really deep, and that’s difficult.”
Diaz was arguably unfortunate not to win a penalty after being brought down by Nathan Patterson shortly before the handball decision.
It is not a position we are likely to see Diaz in much this season, but the decision helped to ensure that the Reds broke down a resilient Everton side in the second half.