I'm currently reading a fascinating book called Soccernomics that says the exact opposite. They reckon that getting more penalties doesn't necessarily mean you win more matches, more likely a by-product of winning more matches. To get a penalty you need to have the ball in the opposition's box, the teams at the top will be attacking more and therefore have a higher chance of winning penalties. These teams would very likely have won the same points with or without the penalties. We know how only the relegated teams could compete with our low goal tally, so that should explain why we only got four.
If you wanted to argue that we need 5-6 stonewallers to get one given, that I would agree with. Although that would mean an additional 16+ penalties which we would surely have won some more points from and would therefore disprove my first paragraph

good book, though!