Malton lost 28-17 to invitation side the Flying Coconuts in the quarter-finals, while The Feathers fell 26-7 to Brookfield.
Malton had off a representative line-up from rugby league outfit Heworth ARLC 34-0 in the first round, but then came a cropper to the Coconuts, a team put together by Beverley captain Junior Tupai.
Coconuts went on to lose their semi-final to another invitation side, Oxfam Crusaders, the overall tournament winners, who edged Northern Exiles 36-34 in the final.
The Crusaders are a bunch of mates originally from Norfolk who now play at various clubs in the South and Midlands. They formed a sevens side in 2012 to raise money and promote the Oxfam charity.
The Feathers had hammered Old Pocklingtonians 47-0 in the preliminary round and surprised York 19-5 in round one, before losing in the last eight.
The tournament was watched by a bumper crowd of almost 3,000 in the Good Friday sunshine, with the plate competition won by Driffield.
Amplefordians had been scheduled to compete but were unable to field a team.
Pocklington 7s results
Preliminary round: Heworth ARLC 24 The Pilgrims 0, Goole 7 Newcastle Brookfield 20, Old Pocklingtonians 0 The Feathers 47.
Round 1: Catterick Fijians 12 Yapham Badgers 7, Oxford Crusaders 31 Selby 0, Flying Coconuts 27 Driffield 17, Malton & Norton 34 Heworth 0, Pocklington 31 Ionians Hawks 19, PFC Olympiakos 0 Northern Exiles 41, Hull Ionians 12 Brookfield 44, York 5 The Feathers 19.
Quarter-finals: Catterick 12 Oxfam Crusaders 27, Flying Coconuts 28 Malton & Norton 17, Pocklington 0 Northern Exiles 20, Brookfield 26 The Feathers 7.
Semi-finals: Oxfam Crusaders 35 Flying Coconuts FC 5, Northern Exiles 21 Brookfield 12.
Final: Oxfam Crusaders 36 Northern Exiles 34.
Plate Competition: Yapham Badgers 12 Selby 26, Driffield 44 Pilgrims 5, Ionians Hawks 29 Goole 12, York 22 Hull Ionians 28. Semi-finals: Selby 5 Driffield 34, Ionians Hawks 29 Hull Ionians 15. Final: Driffield 34 Ionians Hawks 19.