The Northern Irish side missed countless opportunities, including Peter Thompson's 38th-minute penalty, which was well-saved by keeper Meinhardt Joenson.
Mark McAllister also saw a goal disallowed and missed several other chances in a match the hosts should have won comfortably.
The second leg will be played on July 10, with the winners rewarded with a second-round qualifier against AEK Limassol of Cyprus.
The new European season kicked off with two embarrassingly one-sided matches on Tuesday, less than 48 hours after Spain won Euro 2012.
Malta captain Michael Mifsud produced the outstanding performance of the evening with four goals as Valletta crushed hapless Lusitans of Andorra 8-0 in one of three Champions League first qualifying round first-leg ties.
Lusitans, who won the Andorran league for the first time last season, were quickly in trouble as Jonathan Caruana gave Valletta a fourth minute lead.
Former Kaiserslautern, Lillestrom, Coventry City and Barnsley forward Mifsud and Brazilian striker Jhonnattann, signed from Volta Redonda earlier this year, added two goals apiece as the hosts raced to a 5-0 lead after only 23 minutes.
Mifsud made it 6-0 and completed his hat-trick on the stroke of halftime and added another to his tally with a solo goal in the 70th minute before Edmond Agius rounded off the scoring two minutes later.
Luxemburg's FC Dudelange, who got the 2012-13 season rolling as their game kicked off first, thumped San Marino's Tre Penne 7-0.
Dudelange's match kicked off only two days after Spain lifted the Euro 2012 trophy in Kiev to bring the curtain down on the previous season.
Sofian Benzouien and Aurelien Joachim both scored twice for the Luxemburg side who have been domestic champions 10 times in the last 13 seasons.
The Champions League will take nearly 10 months to complete, with four qualifying rounds, a group stage and three more rounds of knockout games, before ending on May 25 with the final at Wembley.