I've been playing this series on and off since about FM2007 and I would say I've been involved in about 250 penalty shootouts. Out of those I would say I have won less than 50. It's not even a coin toss anymore it's basically like trying to win the lottery.
I win most penalty shootouts with my st mirren side, I'm just lucky to have a good 6 or so players with around 15 penalty taking stat, and I've got a great goalie too, I also when it's looking like penalties try to keep on my high penalty-taking players even when they're incredibly tired and sub on people with high penalty taking where possible, even if it means breaking my formation for a few minutes, it's risky, as you could easily concede a late goal, but sometimes it's for the best.
I've actually had a penalty shootout that went to like the 8th player and I was lucky my defender with like 9 penalty taking scored was so thinking I was doomed
One thing to do is to stop the game at full time, then reassess your penalty takers based on current fitness, current morale and game rating. Dont always put your takers in descending order of ability and dont be afraid to put your captain, if he has high attributes for composure and determination and not neccessarily a top attribute for penalties, in the list
I have comfortably won all my penalty shootouts so far. In fact, I actually look forward to them. However, one of my best strikers (Marquinhos) suffered a Roberto Baggio-like heartbreaker by missing the last penalty in a World Cup final shootout. The amazing thing was his morale afterwards was still 'Superb'.
I beat Ghana in the semis of the WC with Turkey in 2014 and looking back at the result here's the takers with the four stats I consider neccessary (Pens, Determination, COmposure and Concentration)
1 Nuri (14/12/17/13)
2 Tuncay (11/18/14/15)
3 Necip Uysal (13/12/15/14)
4 Tarik Uyar [regen] (15/8/13/13)
All scored, nothing special
Now I won fairly easily this time with an only all-right set of players. From this and other shootouts on previous saves and games I believe that there are factors which allow you to beat the AI easily:
1) I think the AI is too narrow in it's criteria, it only really chooses the penalty stat.
2) It always goes best to worst (I mix it up a bit often putting older more steady players before better takers)
3) It doesn't choose it's subs well. Buaben and Dickoh came on early in the 2nd half for better players, who coincedentally were also better pen takers. Dickoh in this case was forced, but the choices were odd, like they were going for the 0-0 and pens, but they didn't have the players on the field to win then.
4) The AI doesn't distinguish on experience either. There were 2 young regens in that list mine and theirs. Their regen went first, mine went fourth. The AI regen was in his second season (admittedly he's a player I'm looking at) at Timisoara, mine was on his third a Fenerbache player on loan at Sporting de Gijon in La Liga (and getting regular starts).
Now on this point I've had a 20 y.o. player scoring 2 on his debut from the spot, but by then he was a seasoned international, and he was only picked as both my main penalty takers weren't playing (one injured one resting). I would never put a player like that first, too much pressure.