The German, who left a role at Lokomotiv Moscow to join the Red Devils, addressed the media after the club cut ties with Russian airline Aeroflot.
United released a statement sharing fans' concerns and Rangnick echoed those sentiments.
He said: "Everybody has the same opinion about what's happening there.
"This is a human disaster what's happened there for all of the people involved.
"Right now, as far as I can tell, he situation in Russia and especially in Moscow is relatively safe but that doesn't change the whole situation which is desperately sad.
"When I watch TV in the morning or the evening I still cannot believe what I see there.
"It's a terrible situation and I very, very much hope that politicians all over the world can help to de-escalate the situation and finish with those kind of things that are happening there."
A commercial partner since 2013, the club decided to end their association with Aeroflot after the UK government banned the airline from flying in their airspace and the Civil Aviation Authority suspended its foreign carrier permit.
The Premier League club said in a statement: "In light of events in Ukraine, we have withdrawn Aeroflot's sponsorship rights.
"We share the concerns of our fans around the world and extend our sympathies to those affected."
United's decision to end their partnership isn't the only major sporting move today, with Rangnick's former club Schalke removing the logo of Russian company Gazprom from their shirts, before UEFA confirmed their decision to strip Saint Petersburg of their role as hosts of the 2022 Champions League final.
The showpiece event will now be held at the Stade De France in Paris, a decision that Rangnick said was 'inevitable'.
He said: "The situation itself is desperately sad. I think everybody will think similarly about that.
"This is an incredible situation that we have that kind of war within Europe and so the decision taken by UEFA was inevitable and it was the right decision."