Miller called time on his Scotland career just over a week after scoring an impressive goal in the 3-2 defeat by England at Wembley.
Mulgrew said: "I am very surprised. He is a good player and a good professional. I am sure he still has a lot to offer and he showed against England how good a player he is.
"He has served the country well and I wish him all the best."
Mulgrew's club manager at Celtic, Neil Lennon, played with Miller during the 33-year-old's spell at Parkhead and backed Scotland manager Gordon Strachan's assertion that the striker's dedication had paid off.
"I think he has been great for Scotland," Lennon said. "I think Kenny deserves anything he gets out of football because he gives everything to the game.
"He gave his all for his country and what better way to go out in his Scotland career than scoring a fantastic goal at Wembley.
"I think he has been an excellent player wherever he has been and I wish him well.
"Maybe his age, the travelling... I have played with him and Kenny is a player who covers a lot of ground in games, he sacrifices a lot for the team.
"He is a real team player so he can walk away with his head held very very high for what he contributed to the Scottish game at international level."
Scotland coach Stuart McCall echoed the praise for the forward's commitment.
The Motherwell boss said: "Gordon rang me last night and I've got to say I'm disappointed. I've not worked with Kenny before but whenever he has come along he has been a great professional.
"I've always liked him. I know he's had his critics but whenever he pulls that Scottish shirt on he gives everything he has got.
"It was disappointing to lose at Wembley but if he has to finish, he has finished on a top-class goal. I wish him well. He's been a great servant to Scotland."
- Sports & Recreation
- Gordon Strachan
- Neil Lennon