The away side started the game very well and were soon 2-0 up through Jordan Hugill and Sean Maguire as they pressed Fulham high up the pitch and forced them into error after error, something the Whites struggled to deal with.
However, Tom Cairney entered the fray at half time and Preston dropped off, allowing the hosts more time on the ball which got them back into the game, first through Norwood's penalty and then through a Denis Odoi last second equaliser.
And despite the poor first half performance, Norwood was delighted that Fulham eventually got level and grabbed a point from the tie.
He said: "I missed a sitter, completely missed the ball and misjudged it and I should've scored to put it 2-2 and Denis got me off the hook.
"We accept that the first half was nowhere near good enough and that it wasn't us but you have to give a bit of credit to Preston, they came and pressed high, were aggressive and won the ball back and didn't allow us to settle into our rhythm.
"We tweaked it a bit at half time and thought second half was a lot better and we were delighted with the point we got last minute.
"In the second half we changed our shaped and got Cairney on the ball a bit more, maybe that gave us a better grip and different positions and as I say, I'm delighted with the point."