Anthony Pelton is correct. Back in 1967 and indeed in 1968 when Manchester United won it for the first time, it was called the European Cup and it was the Champions only of each country that could compete. The League group stages are a relatively new idea. They have tinkered with it a few times over the last few years as they have allowed more teams to be involved in it.
But back in 1967 all the Champions from all the European countries went into a draw like the FA Cup format, and you played over 2 legs, home and away. Back then I think there were 2 or 3 rounds before you got to the quarter final. But it was single elimination all the way through.