An accidental clash of the heads 43 seconds into the third round split Munroe’s right eyebrow resulting in a technical draw.
Munroe had taken the first round while Quigg won the second.
“There were two warriors out there, I wasn’t even warmed up yet, but that’s how the game goes,” Munroe told Sky Sports.
“I’m frustrated I can’t take a belt home for my kids, its Father’s Day tomorrow.
“I haven’t seen the cut yet but I can see the grimaces on people’s faces. I’m fine though. If he wants to go and complete the 12 rounds I’m up for that.
“Obviously the doctor said it can’t be done.”
On the undercard, Sergey Rabchenko won the vacant European junior middleweight title with a seventh round stoppage of veteran Ryan Rhodes.
Rabchenko extended his unbeaten record to 22 bouts with the win, landing a body shot late in the seventh to wrap things up.
"If you get caught in the right place with a body shot, it's over. And he caught me with a brilliant body shot," Rhodes said after the fight.