It is understood that he was convinced he would be allowed to link up with his team-mates once partner Nagore had given birth on Merseyside. But Benitez announced that Alonso would not be travelling.
He added: "He wanted to come out here but only if everything was okay.
"We could not wait and had to make a decision. You cannot wait and wait and wait for any player. There comes a time when you have to decide and make use of your squad."