Chairman Steve Parish said the Eagles were keen on the 21-year-old over the weekend, with Huddersfield Town, Brighton and Hove Albion, Fulham and Rangers also interested.
But with the England international destined for Selhurst Park, Palace have pulled out of the deal due to Solanke suffering from a muscle problem.
The former Chelsea youngster has not played a single minute for Liverpool this season and Hodgson says the club have opted against taking a risk on the forward.
"Unfortunately it is a club decision," he told the media after the 2-0 win over Wolves.
"It turns out there were complications and the club decided it wasn’t the right moment to do it.
"He had made his mind up in our favour, but it didn’t work out. But you accept these things as a manager."
The ex-England boss added to BBC Sport: “The club has taken the decision to move on and we will work with what we have.”
Hodgson was speaking after Palace pulled six points clear of the relegation zone with late win at Molineux over Wolves.
Jordan Ayew, who was said to be under pressure in anticipation of Solanke's arrival, scored his first of the season before Luka Milivojevic completed the win via a stoppage time penalty.
On Ghana international Ayew's first top flight goal since last April, Hodgson added: "When you are a forward you do need goals, and he has had to wait for that.
"If anyone deserved that goal tonight, it was him. He worked hard and defended well.
"We have modified our line up at times, but we have that flexibility to play with one, two or three up front.
"Occasionally, he gets sacrificed in those moments, but it was good to bring him back in tonight."