Goalkeeper Oluehi was dismissed five minutes into the contest - a situation that saw the Super Falcons bow 4-1 against ruthless Dominik Thalhammer's side at the AEK Arena.
Asisat Oshoala's second half strike turned out to be a mere consolation as the weakened African champions paid dearly for their goalkeeper's early dismissal.
And the Swede admitted his side were feeling fatigued after playing for 85 minutes with 10-player as he hopes for improved showing against Slovakia on Friday.
"It was a very tough game with a red card six minutes into the match," Dennerby told Goal.
"We were forced to play with 10 players for the rest of the game and managed a goalless draw in the first half.
"We conceded our first goal from set pieces and after that the players started to get tired. I am sure that we would have beaten them with 11-11 players on the pitch.
"I am happy it's only preparation games and we will work hard to improve on our performance in the next game against Slovakia."
Nigeria will look to recover from their opening loss to bounce back against fourth-placed Slovakia at the Antonis Papadopoulos Stadium on Friday.