But the Blues boss did not feel disappointment at the outcome.
Yeovil’s 2-0 success over Reading Under-23s on Wednesday evening ensured Pompey failed to qualify from the group stage.
It had taken 24 hours for their fate to be decided, now Cook’s men have solely the league to concentrate on.
In a week which also produced an FA Cup exit at the hands of Wycombe, the focus is fixed on promotion.
And for Cook, the latest cup departure is not one to be mourned.
He said: ‘I was there at Reading, I do try to be a football manager from time-to-time!
‘Getting through would have been nice – the reality is we are now out, so let’s concentrate on the league.
‘Personally, though, being out of all the competitions is good, it’s healthy for me and the squad will get rest.
‘As manager of this club, this year I will be judged on the success in the league. Having a clear run at that is great for me now.’
The Blues’ third and final Southern Group A match was a 1-0 victory over Bristol Rovers, courtesy of Kal Naismith’s stunning late strike.
And while Cook has little affection for the competition, he does recognise the influence victory has on his team for tomorrow’s visit of Mansfield.
He added: ‘Nowadays, when you have lost three home games on the bounce people can’t wait to throw it up, so not losing again was probably important.
‘For me it wasn’t important, believe it or not, because it wouldn’t have affected my thought process for Saturday.
‘Whatever happened on Tuesday, we were still fifth in the league and three points off automatic promotion.’