Laudator Temporis Acti

Anacreon 101 Diehl = Greek Anthology 7.160, tr. Guy Davenport, Thasos and Ohio: Poems and Translations 1950-1980 (San Francisco: North Point Press, 1986), p. 69:

He was a soldier in the wars.
Timokritos. This is his grave.
Sometimes blood-drinking Ares kills
Not the cowards but the brave.

Greek has words for blood-drinking and blood-thirsty, e.g. αἱματοπώτης (alt. αἱμηπότης, αἱμοπότης, αἱμοπώτης, αἱμωπός), αἱματορρόφος, αἱμόδιψος, but after a quick search I don't see any of these as epithets for Ares in C.F.H. Bruchmann, Epitheta Deorum Quae Apud Poetas Graecos Leguntur (Leipzig: B.G. Teubner, 1893), pp. 36-43. Ares of course does love blood—he is φιλαίματος in another epitaph attributed to Anacreon (100 Diehl = Greek Anthology 7.226, line 3). But Davenport's "blood-drinking" doesn't appear in the Greek of Timocritus' epitaph:

Καρτερὸς ἐν πολέμοις Τιμόκριτος, οὗ τόδε σᾶμα·
  Ἄρης δ᾽ οὐκ ἀγαθῶν φείδεται, ἀλλὰ κακῶν.

C.M. Bowra, Early Greek Elegists (Cambridge: Harvard University Press, 1938), p. 181, translates the epitaph as follows:

Of brave Timocritus this is the grave:
The War-God spares the coward, not the brave.

Another translation, by Andrew Robert Burn, The Lyric Age of Greece (1960; rpt. Minerva Press, 1968), p. 316:

Good soldier was Timokritos, whose grave
This is. War spares the coward, not the brave.

See D.L. Page, Further Greek Epigrams (Cambridge: Cambridge University Press, 1981), p. 135, who says:

Weber and Friedländer ask why the epigram should be taken away from Anacreon; the proper question was, why should it be given to him? The only witness, the Anthology, is notoriously unreliable in such a case. If the epigram was inscriptional, it was unsigned; and the ascription to Anacreon is presumably the product of guesswork; if it is a pseudo-epitaph, merely a literary exercise (for the sake of the neat pentameter), it is certainly much later than the age of Anacreon.

It is commonly assumed (e.g. by Bergk PLG 3.281, Peek 888, Wilamowitz TG 36 n. 4, Beckby 2.578) that the epigram is an inscriptional epitaph; if it is, it is probably much later than the age of Anacreon, for, as Friedländer observes (Epigrammata p. 69), 'the sententious pentameter has no counterpart on the tombstones, at least in the archaic period'; there is indeed nothing like it in the fifth century.

On the sentiment expressed in the pentameter, cf. Aeschylus fragment 100 (tr. Herbert Weir Smyth):

But Ares ever loves to pluck all the fairest flowers of an armed host.

                                                ἀλλ᾽ Ἄρης φιλεῖ
ἀεὶ τὰ λῷστα πάντ᾽ ἀπανθίζειν στρατοῦ.

Sophocles, Philoctetes 436-437 (tr. Hugh Lloyd-Jones):

War never willingly destroys a villain, but always noble men.

                           πόλεμος οὐδέν᾽ ἄνδρ᾽ ἑκὼν
αἱρεῖ πονηρόν, ἀλλὰ τοὺς χρηστοὺς ἀεί

Sophocles, fragment 724 (tr. Hugh Lloyd-Jones):

My son, Ares loves to kill the noble and valiant; and they who are brave with their tongues escape destructive forces and keep out of trouble; for Ares cuts down nothing that belongs to evil.

τοὺς εὐγενεῖς γὰρ κἀγαθούς, ὦ παῖ, φιλεῖ
Ἄρης ἐναίρειν· οἱ δὲ τῇ γλώσσῃ θρασεῖς
φεύγοντες ἄτας ἐκτός εἰσι τῶν κακῶν·
Ἄρης γὰρ οὐδὲν τῶν κακῶν λωτίζεται.

Euripides, fragment 728 (tr. Christopher Collard and Martin Cropp):

War does not usually achieve all its aims, but rejoices in the deaths of brave young men and spurns cowardly ones. This is an affliction for the city, but glorious for those that have died.

φιλεῖ τοι πόλεμος οὐ πάντ' εὐτυχεῖν,
ἐσθλῶν δὲ χαίρει πτώμασιν νεανιῶν,
κακοὺς δὲ μισεῖ. τῇ πόλει μὲν οὖν νόσος
τόδ᾽ ἐστί, τοῖς δὲ κατθανοῦσιν εὐκλεές.