The Blues, who started the campaign in the hunt for seven trophies, have played more games than any of Europe’s top clubs this season.
Rafael Benitez’s men will make the 2,000-mile journey to Kazan on 11 April for the return leg of their last-eight showdown.
And Hazard, who helped the west Londoners battle back to earn an FA Cup replay against Manchester United last weekend, admits the draw is far from ideal.
“Being totally honest, from a geographical point of view we probably would have preferred a different draw,” Hazard told Chelsea’s website.
“We have to get through and playing in Russia is never an easy game.
“However, we have to make sure we do enough in the first leg to go over there and secure our place in the semi-finals.”
Chelsea take on West Ham United in the league at Stamford Bridge on Sunday – and the Belgian playmaker believes it is crucial the Blues get off to a good start, as fatigue could be a factor later in the game.
He said: “Towards the end of the game tiredness may set in for us, while in effect they should be stronger because they’ve had a bit of a rest.
“It’s something we have to deal with, and with the support of our fans behind us I’m sure we will be able to because three points are a must for us on Sunday, we need to win the match.”
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