Nick Montgomery took Hibs to Ibrox to face Rangers on Saturday and was looking to hand Philippe Clement a difficult start to life as Gers boss.
Hibernian though folded and suffered a 4-0 defeat, something which leaves them on nine points from nine league games.
Miller insists that Hibernian regularly gave away possession cheaply and thinks that they can count themselves lucky they only lost 4-0.
He warned if Montgomery’s men do not cut out playing themselves into trouble, they will be worrying about the wrong end of the table.
“Rangers were good in the press. They won the ball in the Hibs half so many times”, Miller said on BBC Sportsound.
“The longer the game went on, Hibs kept giving it away. They got off lightly with four goals.
“Hibs are one of the biggest teams in the country and they should be challenging at the top end of the table.
“If they continue to play themselves into trouble, they’ll be looking over their shoulder, not up the way.
“There’s a lot of work for Nick Montgomery to do.”
Hibernian now have another big test looming with Celtic set to pay a visit to Easter Road in the Scottish Premiership next weekend.
