In this context reverse means defeat, and is not restricted to football or sport.
Oxford Dictionaries online gives the following for one of four uses of the word as a noun:
An adverse change of fortune; a setback or defeat:
‘United suffered their heaviest reverse of the season’
The OED gives the first example of its use in 1526, and this and other early examples cited there refer to general adverse change in fortune. It suggests ‘defeat in battle’ was its most frequent modern (i.e. early 20th century) usage. So, no, it is not entirely synonymous with ‘defeat’, but can be used in a wider context (although it is somewhat old-fashioned). I imagine that in its original use to indicate a change in fortune, the word ‘reverse’ implied the reverse/opposite/contrary of previous good fortune.