I think this highlights the need for a gross error check before you blast off. There aren't that many things that will quckly kill you on an attempted departure (dramatic failures excepted).
Correct flap setting? Ballpark thrust? Right runway/intersection? Everything else is icing on the cake.
I can fully sympathise with the lack of proper rest - I don't know anyone in LH who doesn't suffer from that every now-and-then; it's also very rare to go 'crew fatigue' as you think you're letting the side down (or in some airlines, setting yourself up for a disciplinary). Most of us say something like: 'Had a sh!t night, let's take this slowly and watch me carefully.'
I wouldn't condemn the Captain out-of-hand, especially as he may not have said all that was reported in the article, or even in the manner it was written. Does seem to be slightly lacking in the 'mea culpa' department, though.