Bournemouth were beaten 3-1 at Brentford in the play-offs (3-2 on aggregate) despite taking a 2-0 lead in the tie.
The match turned when Brentford were awarded a penalty for handball against defender Lloyd Kelly, a decision which left Woodgate bewildered.
When asked about his future after the game, Woodgate told the Bournemouth Echo: “I haven’t thought about it. I’ll be honest with you, I haven’t thought about that.
"I’ll go back and reflect on what went well since I’ve been in charge and what a decent job that we did to get to this stage.
"Okay, it didn’t go fully to plan, for reasons and issues that we can’t really affect, by referees making bad decisions like that.
"It’s been a crazy few months, but it’s something that I’ll think about. Listen, at the end of the day it’s not my decision to make, it really isn't my decision."
Blackburn considering Aynsley Pears’ future
Elsewhere in the Championship, former Boro goalkeeper Aynsley Pears has been linked with a move away from Blackburn.
The 23-year-old has made just three league appearances for Rovers after moving to Ewood Park from Boro last summer.
According to the Sun’s Alan Nixon, Blackburn are open to a loan move for Pears so he can receive more game time.
For that to happen, manager Tony Mowbray would need to sign a new number two goalkeeper.
Watford have been tracking Ashley Fletcher
Finally, it was reported last week that former Boro forward Ashley Fletcher is set to sign a five-year deal with newly-promoted Watford.
According to The Athletic, Fletcher shares the agent as Hornets duo Troy Deeney and Tom Cleverely and has been on the club’s radar since he came through the ranks at Manchester United
The report claims Watford have been aware of the striker’s contract situation and were keen to sign the 25-year-old even if they weren’t able to win promotion from the second tier.
Fletcher was offered a new deal at Boro but will become a free agent when his contract expires in June.