Lomachenko, promoted by Arum, and Usyk, the unified heavyweight champion, were both expected to fight this year.
The former had a deal almost agreed to face George Kambosos Jr for the lightweight titles while Usyk was set to take on Anthony Joshua in a rematch from their September bout in London.
However, both men have postponed any talk of returning in the ring by returning to their homeland to defend Ukraine after the invasion by Russia.
And Arum gave a heartfelt message to the boxers.
"These are two of the premier fighters in our time and the fact that they are not performing now is a real sadness on our part. And hopefully we can see them back displaying their amazing talents in the near future."
Arum also spoke about the courage of his fighter Lomachenko and revealed how his determination to return to his native.
"Vasiliy was, before this conflict broke out, was training in Greece," Arum said. "There's a Russian orthodox monetary in Greece where all the monks are Russian speaking and apparently it's up high enough, you clear your lungs and everything, and he went there after his friend Oleksandr Usyk went there and recommended.
"So now he's in Greece, this war breaks out where Putin's aggression, he is contacted by Egis Klimas, his manager, and his family is still in Ukraine. Now what he could've done was fly - he couldn't fly into Ukraine - so he flew back to Romania and got a car and drove over the border to be with his family and enlist in the defence of Ukraine.
"Now what he could've done if he thought only of himself was to fly into Romania and have his family - which would've been perfectly okay - meet him in Romania and take 'em all back to the United States where he has a house, and he has a green card here.
"So he didn't do that. Why? Because as he told Egis, he felt his obligation was to the people of Ukraine and he was gonna stand and fight against the Russian aggression.
"Now that to me is real heroism. And not that, it hit really in the pocketbook because he's no fool, we had a deal in principle with Lou DiBella for him to fight Kambosos in Australia in June and that fight now is obviously in jeopardy because he is in Ukraine fighting for his people.
"And also there's now an edict that if you're a military age person and Ukrainian you can't get out because you have to fight. But, again, he was out and chose to go back in. So a lot of props for Vasiliy Lomachenko.
"He's my hero and what he did in this situation is demonstrate tremendous courage."
Lomachenko is regarded as one of the greatest fighters to lace a pair of gloves and has won world titles in three divisions.
His amateur career is even more impressive with a 396-1 record, avenging his sole defeat twice on his way to winning two gold medals at the Olympics.
Lomachenko is still hoping to face Kambosos in June according to reports but if it fails to come into fruition then Devin Haney, the WBC titleholder, could step in and take on the Australian.
Usyk, meanwhile, outpointed Joshua to become a two-division world champion in 2021 and became just the third fighter to win world honours at cruiserweight and heavyweight.
Klitschko provides Kyiv update
Major of Kyiv Vitali Klitschko provided an update and predicted around two million residents were still in the city despite continuous attacks made by Russia.
According to Klitschko, civilians are refusing to leave and are instead choosing to 'protect our houses'.
"We see the result of bombing, and civilian people dying," said Klitschko.
"The spirit right now, everyone's angry. I talk to the people and they don't want to leave.
"This activity has brought much more energy to everyone and everyone understands they don't want to leave. We want to defend our city. We want to defend our houses.
"We have - right now - electricity, heating, gas, we have water," he added, speaking in English.