Diaz sustained an injury earlier in the week during Liverpool's training camp in the United Arab Emirates, while Elliott came off in the 29th minute of the Dubai Super Cup opener with Olympique Lyonnais on Sunday.
Speaking at a press conference following the Reds' 3-1 defeat, Klopp said: "Harvey got a knock before we scored, Harvey got a knock. But I think we were lucky.
"He looks fine now but he feels it, that's normal, there was contact. But I hope we were lucky in that moment."
On Diaz, he continued: "Yeah, he was not in the best possible place. It's clear it's a big disappointment for all of us, for him as well.
"It was a non-situation in training, honestly – nothing, felt something. [He] didn't feel a lot next day but we wanted to be really cautious and said, 'OK, come on, let's have a look.'
"Yeah, then the news came and it was a proper smash in the face. But that's it now."