DarkMark has pointed you in the right direction and he has certainly had some great results with his "other suggestions" on his builds.
I will just add a couple of points though.
Goof Off is about 98% acetone (IIRC) and can melt the plastic binding, so be careful not to go too liberally (ie: pouring it on).
Wiping the glue with a rag dampened with goof off and then scrubbing the veneer with a small brass bristled or stiff plastic bristled brush (also available at the Bunnings) then wiping again with the rag is a practical method (repeat until gone).
Secondly, the goof off is going to remove the stain, so you may need to take it all back as much as you can before re-staining so you don't end up with light & dark areas.