The League Cup winners lead Daugava Riga 5-0 after a stunning display in the first leg at Pittodrie.
They now head to Latvia for the first qualifying round's return clash and Hayes insists they are determined to finish the Baltic minnows off in professional style at the Daugavas Stadiona.
The Irish left-back said: "We are going there 5-0 up and a lot of people will think the tie is over - but not us.
"We always knew from the start that this was going to be settled over two legs and two different matches. No two games are similar.
"We have got to go with the mindset that this is still 0-0 and be professional as well as working on our fitness, as we are obviously still in the midst of pre-season."
Riga had two men sent-off in the Granite City clash while Dons midfielder Peter Pawlett limped off with an ankle knock after he was kicked off the ball by visiting defender Giedrius Tomkevicius.
But Hayes is not worried about a repeat of the Latvians' dirty tactics.
"It was tough and there was a couple of red cards which made the match look dirtier than it was," he said. "There was a couple of late tackles on Pete as well but we have got to put that to the back of our heads and go there hoping that it will be a clean game of football.
"There's nothing we can do about how the opposition play."
Baring an unthinkable disaster, Aberdeen should progress to face Dutch side Groningen in the second qualifying round.
And Hayes believes last year's pre-season victory over FC Twente has given Derek McInnes' men the belief that they can continue their march towards the Europa League group stages.
He said: "We have learned a lot about Dutch sides from playing FC Twente in pre-season last year.
"They had the majority of the ball and it was very similar to when you play Celtic.
"We managed to beat Twente though and that set us in good stead for when we played Celtic in the Scottish Cup quarter-final.
"We learned how to play when we don't have much of the ball and that will obviously help us again if we go on to face Groningen in the next round.
"Their players are good on the ball. They are taught that from a young age but we are still on a learning curve.
"However, we are holding out hope after beating Twente last year."