No, and as if you wouldn't question another club anyway, especially one doing better than Liverpool in the league.
Fact is that both those clubs have massive spending power which distorts the transfer fees they are able to pay. Real Madrid might spend £20m on a player and it would be a drop in the ocean for them. However a club like Wigan Athletic spending just half of that would feel the financial effects for a good length of time. Economies of scale and all that.
As for Carroll, I still say Liverpool paid over the odds but they effectively got him and Suarez (now there is a quality signing) in exchange for a player who obviously didn't want to be at the club.