Ashley Burns and Marc Cohen netted for SPEC.
Hendon boss David Garbacz told JC Sport: "For 60 minutes we were in total control of this tie - we went into half time 3-0 up and it could have been at least double that considering the amount of chances we created.
"Some of the football we played in that period was right back to our best, with skipper Ari Last hugely influential in driving us forward.
"But then we slackened off in the final period of the match and they scored two decent goals which was disappointing from our point of view.
"Credit to SPEC who fought hard for the entire match and never let us relax - other teams could well have folded in light of what we threw at them early and they deserved their goals late on.
"We are proud holders of this cup and now we find ourselves in the latter stages of both cups this year after an indifferent league campaign.
"We are more determined than ever to keep these runs going and it will take a very good performance to knock us out."
SPEC FC player-manager Ricky Lawrence told JC Sport: "Going 1-0 down so early was never going to help, but we rallied in the second half despite them making it 4-0 very early and with 10 minutes to go Russell Corin has made a triple save to prevent it being 4-3.
"Hendon are an excellent side who play good football. They definitely deserved the win today and good luck to them in the next round.
"I'm not sure of his name but their number 16 who played right wing was superb for them."
