Pompey climbed into the top three for the first time since September with a 2-0 win at Crawley on Tuesday.
"We've had so much criticism," Cook told BBC Radio Solent. "Some of it is not fair and we all feel it after a bad result or performance.
"That's the way to answer it, with that kind of result."
After disappointing home results against Morecambe and Crewe, Portsmouth moved above Carlisle into third with the win at Crawley.
Second-half goals from Christian Burgess and Kyle Bennett gave Portsmouth all three points.
With 11 games remaining in the season, Cook knows his squad need to keep their focus in the run-in.
"I'm quite a strong character," he said. "I've been around football long enough.
"We've lifted ourselves off the floor so I've said to the lads: 'Let's stay off the floor between now and the end of the season'."
Portsmouth manager Paul Cook was delighted with the nature of his side's response as they moved into the League Two automatic promotion places.