And the Blues’ boss insisted he instead would take the criticism for the result which effectively ended automatic promotion hopes.
York pulled off a thoroughly-deserved 3-1 victory on a night they could have lost their Football League status.
Bradley Fewster and Lewis Alessandra both netted during an abysmal first-half from the visitors.
Luke Summerfield increased the lead shortly after the break before Gareth Evans weighed in with a consolation.
It was the first time the Blues have lost successive league games this season – yet has proven decisive in ambitions to finish in the top three.
But Cook declined to launch into the team which so badly let the club down.
He said: ‘We were outplayed, we have conceded poor goals early on, they were breaking on us at will and we were giving the ball away cheaply.
‘It was a really poor night but my job is to shoulder that blame for the players.
‘If we win games everyone wants to say what a good manager I am – when you lose you must take that criticism.
‘I prefer to take all the criticism that is going because I feel as manager of the club that is my job to do.
‘Just after half-time York were still creating chances, we couldn’t stem the tide.
‘We can talk all night about how bad we were.
‘We haven’t offered up performances like that too much but have done it at a really crucial time. We are all very disappointed but we must move on.
‘I am not going to have a go at anyone, I’m not going to shout and scream at people now.
‘I said in the dressing room after the game it’s important we show character and stand up and be counted.
‘I think at times like this at Portsmouth as manager you have to accept criticism.
‘There are times when everything is going well and everything is great – and times when everything doesn’t go so well and isn’t great.’
To stand a chance of remaining in the Football League, York must win all three of their remaining games – and hope Newport lose theirs.
It’s a tall ask for Jackie McNamara’s men, who had previously gone 12 matches without a win.
And Cook believes they warrant plenty of praise for last night’s display.
He added: ‘York must take all the plaudits because they were absolutely excellent.
‘Credit must go to them. Unfortunately for York the league position deems we get a lot of criticism rather than them praise, that is the way football is.
‘This is our blip at a bad time and you have just got to keep going. We went there and didn’t win the game, now we look to Wycombe on Saturday.
‘And the fans were an absolute credit.’