It is funny how things have shifted since the 1960s. Then FA Cup matches produced far bigger crowds than League matches. League Cup matches generally had worse attendances.
For example the 1965-66 season stands out. City stated the season with crowds of around 20,000 and built up as the promotion drive gathered momentum and ended up at around 30,000. There were a few big crowds in the League, notably 47,000 against Huddersfield on New Years' Day.
In the FA Cup City had 52,661 for a replay against Blackpool. Then the 4th round match against Grimsby attracted 37,918. The Leicester match 5th round match produced 56,787. Everton were drawn in the 6th round and 63,034 tickets were sold out in a couple of hours on a Sunday morning.
Now City can sell out in a league match against Stoke a few days before Christmas but are finding tickets against United in the FA Cup slow to move.
Some things don't change. In the 1965-66 season the lowest crowd of the season was 13,246 against Leicester in the League Cup 2nd round. The 3rd round match against Coventry was not much better at 18,213.
Three years later a match against Liverpool in the 3rd round of the League Cup only attracted around 28,000 although in later rounds there were 40,000 plus crowds.