The Dons drew the first leg of their second round qualifier 1-1 at Pittodrie in their first competitive match and then won 2-0 in Bosnia on Thursday.
"I think I put the tie at risk because I think we were a game short going into this game," McInnes told BBC Scotland.
"I should have played another pre-season game, even at Pittodrie."
With 19 minutes of a scrappy game remaining in Siroki Brijeg, west of Mostar, Aberdeen looked to be going out of the tournament.
An acrobatic Joe Lewis saved had kept out a volley by the hosts' Ivan Krstanovic prior to the Dons scoring their first away goal, thanks to an incisive pass from Ryan Christie and a confident finish by summer signing Greg Stewart.
Six minutes later, Christie set up Gary Mackay-Steven, who stroked the ball home to make it 2-0 and leave Siroki Brijeg needing three goals to progress to play Apollon Limassol next Thursday.
"Thankfully I'm not beating myself up too much because we've got through," said McInnes of his team's preparedness, having arranged pre-season friendlies against St Johnstone and Arbroath.
"The players didn't lose too much fitness, it was more the competitive edge. I would have taken responsibility."
McInnes admitted to a few "scary moments" in the first half as Siroki Brijeg counter-attacked at pace but in truth Lewis was rarely threatened.
The manager, who played Jayden Stockley up front in place of Adam Rooney, added: "We know there is quality in the team. Greg brings a real bit of quality for the first goal and Gary had a fantastic finish.
"You could see the fitness level of the team; we got stronger as the game went on.
"I think that is clearly down to getting the minutes under our belt last week and having another week's training.
"Once we were in front you could see the spirit of the team.
"Our scout has been over tonight in Moldova (watching Apollon Limassol beat Zaria Balti 5-1 on aggregate).
"If we can reach the heights of that second-half performance next week we can be confident going into it. Hopefully the fans get home safely and they can go to Cyprus."
Derek McInnes feels Aberdeen's Europa League victory over Siroki Brijeg was a let-off for him not arranging an extra pre-season friendly for his players.