The Scot was axed by club owners FSG yesterday.
Purslow told BBC Radio 5 Live: "I'm extremely surprised and disappointed. They invested a lot of money in his team and I'm not sure they've given him anywhere near enough time to make the investment work. It seems bizarre to me."
Club legend John Barnes said: "Liverpool have been a good cup side over the last few years but doing well in the league is what it's all about."