The Ibrox side announced in a statement that Allen had left for "family reasons".
The Rangers manager is unsure if an immediate successor will be sought, but he said he will be involved in any discussions.
Speaking after the victory over Livingston, Gerrard said of Allen: “He sold the job for me, not that it needed selling.
"He was the one who came and got me so I appreciate the opportunity from him.
"But I totally respect and understand his decision, he has been away from his family for two years. He came in at a time at this club when it needed shaking up, he was the one who shook it up and get it to the point it is at now.
“He has worked tirelessly throughout the summer to improve the squad and help us qualify for Europe. If you look at where the squad was and the team was to where it is now, I think he has completed the mission the club asked him to do.
"We all have to respect his decision, that’s the way it is. He will always be my friend, and I enjoyed working with him. I have only good words to say about him.”