Fans have been critical of the teams display in last month's 4-1 loss in Estonia but the defender has backed his boss ahead of the return meeting in Belfast on Friday.
"A lot of guys have said they back Nigel and I'm one of them," said Baird.
"He has been fantastic for us. He has been great for our country and great for the players who have worked under him.
"He's always stuck by us and, personally, he backed me and picked me for big games. He has everyone's respect, he's a good coach and I back him.
"The fans know that it was three mistakes for three of the goals against Estonia and that's what really killed us," he added.
"They aren't silly, they know it was one of those nights and I even thought we played well at times. Let's hopes the fans come on Friday and get behind us."