Wayne Rooney had put England ahead early on, with a win enough to send England above their opponents tot he top of the group.
But Montenegro levelled things up after dominating the second half through a goal from Dejan Damjanovic.
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The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.