Striker Niall McGinn and midfielder Peter Pawlett, who recovered from a knock to make the starting line-up, had the Scottish Premiership side’s best chances, both thwarted by goalkeeper Sergio Padt.
Winger Jonny Hayes also recovered from an injury picked up in the first qualifying round win over Daugava Riga and was influential, while Groningen were limited to speculative efforts from distance.
Tempers flared in the second-half as both sides grew increasingly frustrated by their own inability to score but the away side threatened most as the game wore on, with midfielder Rasmus Lindgren shouting just wide after the hour.
Recent Aberdeen signing David Goodwillie came on as a second-half substitute but the striker was unable to get off the mark since joining from Blackburn in front of 16,523 at Pittodrie.
Aberdeen manager Derek McInnes refused to be downbeat, saying: “We set out to win the game that’s for sure, and to be honest we’re not totally satisfied or disappointed with the performance.
“We knew Groningen would be a tough opponent, but I feel we are more than capable of going over there and scoring a goal or two, I have no doubts about that.”
Aberdeen travel to Holland for the second leg with Gronigen on Thursday, 24 July.