The Dons fought out a closely-matched 0-0 stalemate with the Eredivisie outfit in the first leg of their second qualifying round clash on Thursday.
And Irish winger-turned-full-back Hayes believes not conceding at home is more important that taking a lead to Groningen's Euroborg home.
He told RedTV: "When we look back at the tie, not giving an away goal to Groningen will be a big factor.
"If we had said before the game it would end 0-0 we might have thought about taking that but looking back on the match now I would definitely have taken it.
"It will obviously be tough going over there but if we can get the first goal, knowing the players we have and how good we are on the counter attack, it will be a major step in the right direction.
"It was always important for us not to concede and as a defender now I'm quite happy with that."
Hayes expected to be put under the cosh by the visitors but was surprised to see Groningen sit in for much of the match.
The Dons had the best opportunities as Peter Pawlett and Niall McGinn threatened to find the net in the first half but Derek McInnes' side know they will now have to score in Holland if they are to progress.
"Tony Docherty and the manager have done their homework on Groningen so I'm sure they will have done their homework on us," said Hayes.
"They will have watched the videos of us and know how good we can be on the attack. We have got some players with some fantastic movement and fantastic pace.
"So you could see them came to limit us. But that's not what we expected, knowing how Dutch sides play. We expected them to come at us a bit more.
"I thought we dealt with their threat and nullified them - they didn't really look like scoring.
"I know Jamie Langfield had one or two saves to make near the end but as a team we defended well. We maybe could have attacked a bit more ourselves but we are happy with the result."
The prize for the eventual winner of this tie is a third qualifying round meeting with Spanish big guns Real Sociedad but Hayes insists Aberdeen are scared of no-one.
Speaking before the draw, he said: "If we do get through we will will know we have beaten a very good Dutch side so we will have no fears about who we get in the draw."