A drop goal from Lolo Liu ended the deadlock in what was a mammoth match where both sides held on intently, but it was the IRB Sevens World Series title at stake for Samoa which seemed to galvanise them in the final seconds.
England came back from a 7-0 half time deficit with a try from Tom Powell (Unattached) keeping them in the game and on the full time buzzer Greg Barden (Royal Navy) cruised over the line to give his side the draw, Ben Gollings (Gold Coast, Australia) had a chance to clinch victory but the conversion hit the posts, taking the match into extra time.
Both teams had their opportunities during extra-time, with England showing some great defending under pressure, but tiredness seemed to take over and errors crept in.
James Rodwell (Moseley) and Nick Royle (Fylde) were yellow carded and England couldn't find the space they needed for the crucial try.
England Sevens Coach Ben Ryan said, "I couldn't have asked much more from the players really. That was 10 minutes of extra-time with two yellow cards where we were down to six men on two different occasions, which was pretty tough and I can't fault the players for that.
"But to come so near yet so far is pretty galling really and it was another one of those days where we didn't have the rub of the green."
Samoa secured the 2010 IRB Seven World Series title with a 41-14 against last weekend's London Sevens winners Australia in the cup final.
England Sevens: Tom Powell (Unattached), Micky Young (Newcastle Falcons), James Rodwell (Moseley), Uche Odouza (Unattached),Ben Gollings (capt, Gold Coast, Australia), Mat Turner (Bristol Rugby), Greg Barden (Royal Navy)
Replacements: Nick Royle (Fylde), Oliver Lindsay- Hague (Harlequins), Rob Kevin Barrett (Saracens)
Scorers: Tries: Tom Powell, Greg Barden; Cons: Gollings
Sin Bin: James Rodwell, Nick Royle
England's Emirates Airline Edinburgh Sevens results:
England 17-5 Portugal
England 19-24 Canada
Australia 21-21 England
Cup quarter final England 19-7 Scotland
Cup semi final Samoa 15-12 England