This pattern expresses resignation or frustration: even if you do the action, it won't lead to a good result, so there's no point. It's often used when you're trying to convince yourself or someone else to stop worrying or trying too hard about something that can't be helped.

The meaning is similar to ても無駄だ (even if doing it is useless), but しょうがない carries a sense of 'it can't be helped' or 'there's no alternative.' When you use てもしょうがない, you're saying that the effort is wasted because the outcome won't improve. This can apply to past regrets: even if you think about what you should have done, it won't change what happened.

It's a common spoken pattern, not particularly formal. In writing, you might see ても仕方がない, which is slightly more formal but still acceptable in speech. Use it when you want to say 'it's no use crying over spilt milk' or 'there's no point in worrying about that.'