Tant pis = Oh, well / Too bad (accompanied, optionally by a resigned sigh) when the speaker is addressing her or his own situation.
In my experience, however, when directed at someone else -- and especially when accompanied by the infamous "Gallic shrug" -- it means something more like "Well, that's your look out" (sous-entendu: "I don't care". This is the "tant pis" uttered by the officious railway official who will not let you onto the platform when the last train is about to depart.
-- "But if I miss this train I'll miss my flight too"
-- (Shrug) "Tant pis".