McKenna said: "It's an advantage that Liverpool only found out about the game a month ago.
"It also helps that we've had European fixtures at this time of year for the past six seasons.
"I hope they are not quite ready and underestimate us. If we play out of our skins we might give them a game, but it could be a huge mismatch."
TNS players trained at Anfield yesterday ahead of tonight's televised clash with the European champions and hope they can leave Merseyside with a result that will set up the second leg at Wrexham's Racecourse ground in just six days' time.
"I am under no illusions. I know exactly how hard this will be for my players," added McKenna.
"But I am a proud person and a professional person and I don't want to be humiliated by anybody."