The team had qualified for the UEFA Cup by finishing fifth the previous season, but went out in the third round to Red Star Belgrade.
In the transfer market, Neill brought in Brian Talbot from Ipswich Town halfway through the season to strengthen Arsenal's midfield, especially with a tough cup run.
They faced Lokomotiv Leipzig, Hajduk Split (a game which brought Liam Brady's first goal in Europe), and Red Star Belgrade.
The Serbian side won 2-1 on aggregate, and the crucial last minute goal was scored by Dusan Savic at Highbury.
Arsenal's toughest opponent in the run up had been Third Division side managed by Jack Charlton, Sheffield Wednesday.
Talbot made his FA Cup debut in a 2-0 defeat of Notts Country before Arsenal faced Brian Clough's Nottingham Forest in the fifth round.
After the season, Brady announced that he would leave the club when his contract ran out in 1980, hoping for a new challenge in European football.
[9][10] Note: Flags indicate national team as defined under FIFA eligibility rules; some limited exceptions apply.