Niall McGinn and Peter Pawlett had the hosts best chances of the match, but were unable to find a way past visiting goalkeeper Sergio Padt.
The Aberdeen defence, meanwhile, were able to limit their opponents to long-range efforts, which Jamie Langfield was also equal to.
Derek McInnes was able to field his normal starting XI with Jonny Hayes and Pawlett recovering from knocks sustained in the first round qualifying victory over Daugava Riga.
Groningen, who finished seventh in last season's Eredivise, named two new signings in their starting line-up, with former Ajax striker Danny Hoesen and goalkeeper Padt making their debuts
Both midfields cancelled each other out in a cagey start, however it Aberdeen that threatened first on 12 minutes.
After patient build-up play McGinn released Pawlett down the left and the midfielder's shot was parried by Padt and then bounced off a defender for a corner that came to nothing.
With Willo Flood and Pawlett looking lively, Aberdeen continued to apply the pressure on their Dutch opponents with Padt being forced to come off his line quickly to deny McGinn and then did well to keep out a header from Hayes.
The home side had an appeal for a penalty waved away when captain Russell Anderson felt he was fouled in the box, but the Portuguese referee Hugo Filipe was unmoved.
With the first half looking to be fizzling out as quietly as it had begun, Groningen almost sneaked a crucial away goal just before the half-time whistle.
Full-back Hans Hateboar got the better of Hayes for pace down the right-hand side, his cutback was deflected off Mark Reynolds, but Langfield was on hand to save the defender's blushes. The loose ball then fell to Hoesen, who from a tight angle was unable to convert.
The second half started in similarly low-key fashion as the first, but began to get a bit heated with Pawlett and Hayes continuing to be the victim of unfair challenges.
Groningen had two players cautioned as tempers began to flare, first Nick van der Velden was given a yellow for a challenge on Hayes, while defender Johan Kappelhof picked up a booking for a foul on Ryan Jack.
On 62 minutes the visitors threatened again from long range, this time the midfielder Rasmus Lindgren found space on the edge of the box and he fired in a low shot that Langfield was forced to beat away for a Groningen corner.
Adam Rooney made way for Aberdeen's latest summer signing David Goodwillie, much to the delight of the 16,523 Pittodrie crowd, however the former Dundee United and Blackburn striker could not fashion the breakthrough goal.
In the closing stages of the half it was Groningen once again who almost stole an away goal. The two substitutes Jarchinio Antonia and Dino Islamovic linked up well, with the latter flashing a shot the wrong side of Langfield's near post.
It is not the worst result for Aberdeen, but they will now swap their usual surroundings of the north-east of Scotland for the north-east of the Netherlands, as they look to continue their European campaign.