The pair were the highest seeds in action on the opening day of the Romanian WTA International clay-court event, but fell to Monica Niculescu and Lara Arruabarrena - opening up the draw nicely for home favourite and top seed Simona Halep.
Third seed Koukalova crashed out of Wimbledon at the second round stage to Madison Keys late last month and things worsened for her on Monday, as she double faulted nine times in her straight-sets defeat.
Niculescu fed off her home support to reel off the last eight games in a row and wrap up a comprehensive 6-3 6-0 victory. She will now face Alize Lim in round two.
Arruabarrena then disposed of fifth seed Beck - who is 61 places above her in the world rankings - despite losing the first set.
The Spaniard hit back from a 6-4 reverse in the opener to take the second 6-2, before then surviving a Beck revival - which saw her level at 6-6 after being 4-1 down - by winning the third-set tie-break 7-5.
Arruabarrena will face Cagla Buyukakcay next after the Turkish world number 164 swept aside Paraguayan opponent Veronica Cepede Royg 6-3 6-3 in the opening match of the competition.
Sixth seed Anna Schmiedlova was another of the fancied players to tumble out - going down in straight sets (6-3 6-3) to world number 166 Kristina Kucova.
Polona Hercog, seeded eighth, avoided an early exit with a 6-4 6-3 over Anna Tatishvili, while there was further joy for the home crowd with the progression of Romanian wildcard Cristina Dinu.
Following Niculescu's impressive triumph earlier in the day, Dinu proved too strong for Nadiya Kichenok in a straightforward 6-0 6-3 win.