Does this happen to anyone else when your leading or drawing away to a bigger team than you and they get a last minute goal to win or draw because it's happening to often to me. So wondering is it me or is it the game.
Try to avoid your players tiring too much by the end of the match and try to have level appropriate levels of concentration as a minimum.
Combination of the two plus a bit of tweaking to tactics if you're starting to come under pressure (my personal routine is to send the ball down to their corner flag and see if I can hit them on the break) should see the game out.
It's something which you can also take advantage of in AI teams ;)
If you've got a bit of pace up front or on the wings, clear ball to the flanks via shout can be effective. Sometimes shutting up shop will nullify the threat, sometimes playing on the counter will be far more effective, sometimes holding onto possession is the way to do it. Have a look at what they're attempting to do and figure out how to stop it. But if you're consistently giving away late goals, I'd suggest looking at lowering your level of pressing and/or rotating your players a bit more to avoid them being shattered by the end of the match.
Really does depend on the circumstances - no magic bullets sorry.