It's not like the PL has some god-given right to the top 4 making it, plenty of leagues like in France or the Netherlands have less teams make it, and it's always been clearly stated that only the top 3 are guaranteed a spot from the premier league. If you are talking about the fairness of being told there were 4 spots and then losing one just after the season was over, it's not like Spurs and Arsenal didn't know the possibility existed during their run-up. Every team was well aware of the possibility beforehand, so they were all playing by the same rules.
In any case, even if they did want to add Spurs for the money, how would they add one team into the qualifying rounds? Would you add them at the expense of a team that came in 2nd in a smaller league, or force some random team into a playoff with Spurs to just get into the qualifying round? How would that be any more fair?
Having said that, if we had finished 4th, I know I'd be up in arms right now screaming at the injustice of it all.