The Uruguayan forward completed a £75 million move to Barcelona yesterday, although it is not full clear how the Spanish club will pay the transfer fee in full.
Carragher believes the 27-year-old will find it more difficult to adapt to life at Camp Nou, with Lionel Messi's brilliance dictating where and how everyone else plays around him.
For that reason, the former Reds defender thinks Suarez would have ended up at the Bernabeu, where he would be a direct replacement for Karim Benzema.
"I thought a move to Real Madrid would have been more natural for him," Carragher wrote in the Daily Mail. "Yes, [Cristiano] Ronaldo is the star but Luis is a better player than Karim Benzema and he would have played in his rightful position - straight down the middle.
"Liverpool will desperately miss him, there can be no disputing that, but the time was right for him to leave and the club have got the best cash deal they could, as was the case when Torres headed to Chelsea in January 2011."
Carragher had already expressed his views on Liverpool's Suarez sale over Twitter, stating that the Uruguayan was the best player he had ever played alongside.
Meanwhile, in the same column, Carragher also admitted that Arsenal legend Thierry Henry was the best player he ever played against.
"Look at Thierry Henry," he said. "He is arguably the Premier League’s greatest player, certainly the best I played against, but he never showed the same wow factor after he left Arsenal."