It's a number's game. To fill the first slot, the losing team has a 2 in 5 chances of having scored the first goal, since there are 5 goals in total and 2 goals were scored by the loser.
Alternatively, the total arrangements of goals can be seen as WWW (3 goals for the winning team) and LL (2 goals for losing team). The total number of ways of arranging WWWLL, taking account of identical items is 5!/ (3!*2!)=10 ways.
Since the first spot goes to the losing team, there will be a total of 4 goals to be arranged (WWWL) and the number of ways is 4!/(3!)= 4 ways.
Therefore probability of losing team scoring first is # favorable outcomes/# total possible outcomes = 4/10 = 2/5.
+1 Kudos me - I'm half Irish, half Prussian.