Kanoute, on target in his first friendly outing at Forest on Saturday, opened the scoring in Seville's Olympic Stadium.
Meanwhile Edman, our new Swedish left-back, came on for Stephen Carr at half-time with Mauricio Taricco switching to right-back.
Michael Brown also completed 58 minutes on his return from a knee injury.
We started this semi-final well and looked on top mid-way through the first half. Kanoute opened the scoring after 27 minutes, a fine, low, finish from 10 yards following Brown's inch-perfect pass.
It could have been 2-0 minutes later as Rohan Ricketts picked out Kanoute in space at the far post but a towering header was met with an equally good tip over by Babos.
We were on top at that stage only for Feyenoord to enjoy a slice of luck to equalise just before the interval. Kuyt picked the ball up in space, carried forward a few yards and saw his shot deflect off Gary Doherty beyond the despairing dive of Keller.
The second half was disappointing as a spectacle with little goalmouth action at either end.
Jermain Defoe, on for Kanoute, did well to lose two defenders before poking at goal from 20 yards, tipped aside by Babos.
But Feyenoord finished the stronger and just a minute after Keller clawed out Mtiliga's snapshot, Kuyt grabbed the winner. Castelen did well down the left flank and Kuyt dived in at the near post to head home his low cross, 69 minutes on the clock.
MINUTE BY MINUTE GUIDE
2mins: Early burst from Brown, ball fell kindly for him but sliced shot wide.
4mins: Redknapp attempted acrobatic volley no power.
11mins: First save as Keller palms out low Goor free-kick.
16mins: Buffel break down right, cross blocked on the slide by Bunjevcevic.
18mins: Smolarek dipping volley from angle straight at Keller.
21mins: Kanoute into box, rolled ball back into path of Bakari who dragged shot wide from 17 yards.
24mins: Kanoute lost marker but shot wide from 22 yards.
27mins: GOAL. Bakari won header on edge of box, Brown slipped pass through to Kanoute who slid under keeper from 12 yards. 1-0.
36mins: SAVE. Lovely cross from Ricketts met by Kanoute at far post, free header on reach from 10 yards, Babos tipped over.
40mins: GOAL. Kuyt in space, 30 yards out, shot deflected wickedly off Doherty beyond reach of Keller. 1-1.
Half-time: Spurs 1, Feyenoord 1
Half-time: SUBS. Edman, Mendes and Defoe for Carr, Redknapp and Kanoute.
58mins: SUB. Gardner for Brown.
59mins: Bakari inches away from superb Marney cross.
65mins: Defoe made something out of nothing, shrugged off two challenges before poking shot from 20 yards that Babos did well to save.
68mins: SAVE. Mtiliga one-two with Kuyt and snapshot from 18 yards but Keller clawed away at full stretch.
69mins: GOAL. Castelen cross from right, Kuyt diving header from six yards, Keller no chance. 1-2.
70mins: SUB. Jackson for Marney.
79mins: Best move of second half ended with Kalou firing straight at Keller from 20 yards.
81mins: SUB. Hughes for Ricketts.
85mins: SAVE. Kalou through but Keller out quickly to save at his feet.
Injuy time: Bakari tame header wide from Jackson's corner.
Line-ups: Spurs: Keller, Carr (Edman, 45), Taricco, Redknapp (Mendes, 45), Bunjevcevic, Doherty, Marney (Jackson, 70), Brown (Gardner, 58), Kanoute (Defoe, 45), Bakari, Ricketts (Hughes, 81). Subs: King, Fulop, Silva, Ifil.
Feyenoord: Babos, Bosschart, Chali, Kuyt (Lazovic, 78), Buffel (Kalou, 45), Goor (Magrao, 62), Mtiliga, Smolarek (Castelen, 58), Paauwe, Loovens, Gyan (Zuiverloon, 45). Subs: Lodewijks, Ven der Berg, Pardo.
Erik Edman made his debut and Fredi Kanoute bagged his second goal in two friendlies but we lost out to Feyenoord in the Kappa Cup in Seville on Tuesday night.