The Liverpool chief said: "Great players will always leave great clubs, that's happened in the past and will in the future.
"It's up to us to add players that can help support Luis and move us on.
"I have had great support from Luis since I've been here.
"He has really bought into what we are trying to do and our objective has to be to keep the best players. I am safe in the knowledge that Luis had the chance to go in the summer.
"There was probably no better time for that, with a new manager coming in.
"Luis could have had an excuse to go but, having spoken to him at length, he committed to stay."