Barcelona paid a fee in the region of £75m to bring the Uruguay international, who joined the Reds in January 2011, to Camp Nou earlier this summer.
The manager told talkSPORT: "Luis was a fantastic player, a world-class talent and whatever issues he brought off the field, he was a sheer joy to work with.
"He obviously let himself down a number of times and it was the right time for him to go from here. But we've brought in a number of players this summer. We put it into context and we needed the players.
"In the time I've been here and with the money that's been spent we've gone from seventh position to second position in two years and that's with a lot less budget. The budget has been really trim here."
Liverpool have brought in eight players so far this summer, and are expected to complete the signing of Alberto Moreno from Sevilla soon.