Despite dominating the game for long periods, the Bundesliga outfit had to settle for just a point, with Alexander Ring, Hanke and Granit Xhaka all going close, before Wendt's spot-kick struck the bar.
After the disappointment of missing out on the UEFA Champions League, Gladbach began their first game in the Europa league at almost break-neck speed and could have been two goals up in side five minutes. Ring ignored Hanke and shot wide of goal with just 28 seconds gone on the clock, before the striker was then desperately unlucky to see his low drive strike the post.
After their bright start, Gladbach took their foot off the pedal somewhat and Marc-Andre Ter Stegen had to be alert to deny Limassol's Rui Miguel with a brave close-range stop, before his opposite number Matias Degra was forced to turn Tolga Cigerci's free-kick around the post.
The game became suddenly stretched in the opening stages of the second half. Edmar's powerful shot from distance drew a smart stop from ter-Stegen at one end, while substitute Xhaka had a header well saved after Patrick Hermann's precise cross at the other.
Xhaka's introduction had given the away side an extra dimension and he was again involved as Hanke lashed an angled effort wide of the target. Yet the hosts remained dangerous on the break themselves, with Maykon blazing over the bar after a scramble in the six-yard box.
Just as it seemed neither side would force a winner, Gladbach were given a penalty when Herrmann's cross struck the outstretched hand of defender Paulo Sergio. Wendt stepped up confidently but his effort struck the underside of the bar with Degra beaten meaning the Foals now face an even tougher test on Matchday 2 when they host Turkish side Fenerbahce likely needing to win.
Limassol: Degra - Airosa, Dosa Junior, Parpas, Maykon (76. Luciano Bebe) - Dede, Nicolaou - Rui Miguel - Edmar (71. Paulo Sergio), Vouho (58. Orlando Sa), Gilberto. - Trainer: Christodoulou
Mönchengladbach: ter Stegen - Jantschke, Brouwers, Dominguez, Wendt - Nordtveit, Cigerci - Herrmann, Ring (79. Rupp) - Hanke (82. De Camargo), Hrgota (46. Xhaka). - Trainer: Favre