The midfielder was one of the players who quit the club when McCoist's side dropped down into the Third Division last season, but has seen his former manager take the Light Blues to the verge of the League One championship this campaign.
McCoist has not had his troubles to seek during a turbulent time at the helm but Edu is confident he will get the success he deserves in the top flight.
The American international told SportTimes: "Ally is a Rangers man through and through and will always do what is best for the club.
"It would have been easy for him to say 'this isn't what I signed up for' and turned his back on the club but he has stuck true to Rangers.
"His passion for Rangers is evident, it is the club he supported as a boy and went on to play for and now manage.
"Despite the fact that they are where they are, and in an ideal world Ally would like to be managing them in the top flight and competing in Europe, he will stick by the club. He has been great for the club through it all.
"He is building a team to get back to the top flight and I am sure they will compete when they get back there and get back winning leagues and trophies.
"He deserves a lot of credit and the players do too, they are fighting every day to get the club back to where they belong."
Rangers will claim their second successive title in a matter of weeks when they wrap up the League One crown and complete another step on their journey back to the top of Scottish football.
Only Lee Wallace and Lee McCulloch remain at the club from Edu's trophy-laden time in Glasgow but the American can see promise in the next crop of potential Premiership champions.
He said: "It will be different for Rangers winning promotion back to the top division because that is where they deserve to be and they belong.
"They want to get back winning leagues and cups as soon as possible.
"As soon as they are back, they will be there fighting and challenging Celtic for the title and get back to where they belong - as champions.
"You always want to keep players like Lee Wallace and McCulloch, not only for their ability on the field but their influence in the dressing room.
"They are leaders and help bring along the newer players and the younger guys.
"I have watched some of the games and they have a good team.
"The manager has done a good job in developing the team that he has there.
"He has the right players there and he will keep building the team."