The Blues suffered Home Park agony last night as Peter Hartley’s stoppage-time goal ended their play-off bid.
It inflicted an aggregate 3-2 defeat and condemned Pompey to the bottom division of the Football League for a fourth successive season.
Plymouth were worthy winners on the evening and will now contest a Wembley final with either Accrington Stanley or AFC Wimbledon.
Irrespective of last night’s outcome, McInnes has been impressed with Cook’s maiden campaign which ended in a sixth-place finish.
And the Blues chairman is convinced next season the former Chesterfield boss can build on that platform.
He said: ‘Absolutely we are still backing Paul, 100 per cent.
‘He’s a top man, the right man for the job and I think he’ll take us forward.
‘I have said it before and I’ll say it again – he was probably two appointments too late for us.
‘So blame me for that if you would like to, I will take that responsibility.
‘But the truth of the matter is next year we come back fitter, stronger, more talented, more entertaining, more everything really.
‘I think he has done a really good job.
‘There is a comparison with Harry (Redknapp) on this one in so much as he was able to come in and turn the team upside down to get promotion.
‘But people seem to forget Harry sat in the stands for six months before that to ascertain what he felt he needed to do.
‘As far as I am concerned, the board have never had one minute’s doubt that Paul is the right man for the job.
‘And we will continue to support him in any way we can.’
Last season Pompey finished in the lowest placing in their Football League history.
This time around they reached the League Two play-offs, along the way playing plenty of entertaining football.
Last night’s play-off semi-final defeat at Home Park arrived six years to the day since Pompey’s last visit to Wembley in the 2010 FA Cup final.
Now they must seek to strengthen the squad to launch another promotion assault next term.
That will be with Cook once again at the helm.
And McInnes believes now is the time for calm and reflection, rather than any knee-jerk reaction.
He added: ‘It is a time for cool heads. It is a time for reflection, it is a time to be depressed to be honest.
‘Today we will have woken up realising there is another long campaign ahead of us.
‘But the truth of the matter is that is what we have to face up to.
‘In life we do it and in business we do it and in football we have to do it.’