Not if they are 'genuinely' knackered. But if an international athlete played 80 or 90 minutes of football on wednesday or thursday, would he be too knackered to perform at the weekend? There would have to be something physically wrong with him if that was the case.
It's usually less about the game and more about the travel compunded with the game. Flying from Liverpool to Russia takes a lot out of a player, and they usually begin the game jet-lagged and tired before they've even kicked a football. It usually takes about 2 or three days to aclimate to a new time zone (there usually only over for 2), and flying alone can be physically draining. Then they play football, fly back, and they have to fly back and re-adjust with another game in 3 days. It is physically demmanding.
That all said, we did better this year with EL footy than we did without it last year. Saying good ridance, let's not bother is a loser attitude, IMO. 5th is certainly attainable, and 4th is an outside possiblilty. Coming off a 5th place finish with EL footy next year would be something to build on. With a few more squad additions we might even have an outside shot at winning the thing next season. I personally love European night. The last leg of the Zennit game was a heart-breaker, but what a game! It felt like I was really supporting the Liverpool I remembered again.