Hartlepool United sacked Lee following a ‘significant downturn in results and performances’, the club announced on Thursday night.
The shock decision came ahead of the final game of the League Two season, Colchester United at home on Saturday, with Pools already safe.
The club has confirmed Michael Nelson and Anthony Sweeney will take the team for the final game at the Suit Direct Stadium on Saturday.
Woodgate, speaking to BBC Tees, has hit out at the ‘ridiculous decision’ to sack Lee and argues he wasn’t given enough time and should have been given more time and support to revamp the squad.
Woodgate said: “I can't understand the decision but that's football.
“Spike did a good job, he went in there to keep them in the league and he did that.
“In football, first time managerial job for him, and he is given five months and one transfer window.
“What are you supposed to do?
“It is a ridiculous decision, in my view.”
He added: “Why get rid of him so quickly? Give him a chance, you need time.
“They stayed in the league and can rebuild and they are looking at expanding the recruitment department for next season, that's what you need.
“At least give Graeme a transfer window to build a squad. There will be people who will want the job, that’s for sure. Who knows who will get it?
“That’s football. I think it is a horrific decision.”
And pressed on whether he would be interested in the job, Woodgate replied: “Absolutely no chance, they have just sacked my pal. Why would I do that to my mate. It is not something I would look at, no chance.”
Explaining the decision, a club statement outlined clearly the reasons behind Lee’s sacking: “Since losing to Rotherham United on 9th March, the team has won only one of 11 games, picking up just seven points and scoring eight goals.
“Additionally, previously strong home form has not been maintained with no home win since 15th February, resulting in just three points and only three goals in seven games during this period.”
Pools haven’t won at home on a Saturday since October.
And Pools owner and chairman Raj Singh has outlined his reasons – with the board ‘increasingly concerned’ with the form and results.
Singh said: “While we had some great results and occasions in cup competitions, unfortunately, our league performances have not been good enough with only seven wins since Graeme joined the club and as a board we have become increasingly concerned by the drop-off in form.
“This has not been an easy decision to make.
"Graeme is a really good person and he has given everything to the job. I would like to place on record my thanks to Graeme for his efforts and I wish him and his family well for the future.”
Pools end their campaign at home to Colchester United on Saturday.