The combative midfielder, who played a key role in the heart of England U17s European Championship success in May, was named among the substitutes for the visitors before being thrown into the action midway through the second-half.
He impressed after coming off the bench, but he left disappointed as he was penalised late on for a foul in the box that allowed the hosts to seal a 2-0 win.
As to be expected in a season’s opener, the match started in lively fashion with Millwall bursting out the blocks and they were rewarded for their efforts inside ten minutes.
Mark Beevers opened the scoring on eight minutes, stretching to knock the ball into the net from Lee Martin’s corner.
The visitors’ best chance to draw level came against the run of play through Luke Murphy as half-time approached. The wide man broke clear of the defence moments before the break as he honed in on goal in front of the Cold Blow Lane end – but he skewed his effort well wide of the post.
Chances were few and far between in the second half, and it remained just the one goal in it as Cook made his introduction to replace Souleymane Doukara on 64 minutes and took his place down the right of United’s midfield.
A Dominic Poleon strike from an acute angle was brilliantly saved as the away side pushed for a comeback, with Cook finding himself free out wide twice to fire in crosses which were cleared both times – but he was to have an impact on the next goal, albeit not the one he wanted.
As the clocked ticked inside the last five minutes, the unfortunate Cook’s pass to Jason Pearce was not anticipated by the centre-half, and Millwall capitalised on the counter. In a desperate bid to stop Lee Gregory, Cook had rushed back into the area but caught the striker to send him tumbling to the ground – leaving the referee with no option but to point to the spot and Shaun Williams made no mistake with the subsequent penalty.
Determined to make amends straight away, Cook was right back into the thick of it from the restart, but his sizzling strike from 20 yards whizzed past the post – which turned out to be the last action of the game.
Leeds head coach, David Hockaday, said afterwards that he believes his youngster will learn a lot from his experiences at The New Den.
"He gave a poor square ball away, he knows that. He's rescued it and made them play back from a dangerous position, and there was no contact [for the penalty]," Hockaday said in his post-match press conference.
"He's a very talented player, only 17-years-old, and me having to bring him on probably shows you where we are strength-wise.
"But for Cooky, it's a great experience , and in years to come he'll learn from this and he'll become a better player for it."
Elsewhere in the North East, England Under-21 boss Gareth Southgate returned to his former stomping ground to watch Middlesbrough defeat Birmingham City 2-0 at the Riverside Stadium.
Boro defender Ben Gibson, who represented Southgate’s side at the Toulon Tournament in the summer, will have been hoping to impress ahead of next month’s Euro qualifiers with Lithuania and Moldova, but his afternoon was cut short as he limped off after three minutes.
U20 international Adam Reach was on the wing for the home side, with Luke Williams coming off the bench late on.
Fellow wide man Demarai Gray, an U18 international, went closest for Brum, clipping a 30-yard free-kick just over the bar.
Will Hughes played 53 minutes for Derby County as the Rams got their season off to a winning start, defeating newly-promoted Rotherham United 1-0.
England U18 midfielder Dele Alli played the full 90 as his MK Dons side came from two down to record an impressive 4-2 victory over Gillingham.
In the late kick-off, Cauley Woodrow and Patrick Roberts, U21 and U17 internationals respectively, were unable to prevent Fulham from going down 2-1 at Ipswich Town as they both appeared as second-half subs.