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'."

Pakistan finished the second day on 97-8, 332 runs behind Australia's first innings total of 429 at the Gabba.
Hazlewood took 3-19, including two wickets in two balls, while Starc finished with figures of 3-45.
Earlier, Nathan Lyon and Jackson Bird put on 49 runs for the final Australian wicket after Peter Handscomb completed his maiden Test century.
Mohammad Amir finished with 4-97, his best bowling figures since his return to Test cricket in July following a five-year ban, while Wahab Riaz took 4-89.

Maureen Bannister, from Leuchars, had not been seen since about 14:00 on Sunday. It is thought she had been walking her dog in the area of Tentsmuir Forest in north-east Fife.
On Monday evening, a body was found on Tentsmuir Beach by a member of the public.
Police have said Ms Bannister's death is being treated as "unexplained".
Sgt Gary Combe said: "Our sincere condolences go to Maureen's family and friends at this very sad time.
"We're working to establish the full circumstances surrounding Maureen's death and are asking anyone who may have seen her since Sunday afternoon to get in touch."
Anyone with information is asked to contact Police Scotland on 101.

The 24-year-old, who has 26 caps for his country, has signed a deal, subject to a medical, until May 2018.
Sarto said: "Glasgow Warriors are a massive club and play a great style of rugby.
"I wanted to move to the UK as I know the standard of rugby is high and I want to improve my game. Joining a club like Glasgow will help me do that."
Sarto knows Warriors well, having played against them for Zebre in the Pro12, and scored a try when making his international debut against Scotland in the South African Quadrangular Tournament in 2013.
"I've always known Glasgow is a great club and I know Simone Favaro is enjoying it there," he said of the 27-year-old back-row forward.
"I hear the fans love him and I hope I will have a similarly good relationship with them when I move over."
Glasgow head coach Gregor Townsend said Sarto was a player Warriors "had been tracking for a while".
"Leonardo has been one of the best wingers in the Guinness Pro12 over the past few seasons and has an ability to break tackles," he added.
"He has also performed well at Test level and had an excellent all-round game against Scotland last month.
"We believe that he will make further improvements in our environment and will add to the competition for places in our backline."
Portsmouth manager Paul Cook was delighted with the nature of his side's response as they moved into the League Two automatic promotion places.
[NEXT_CONCEPT]
Josh Hazlewood and Mitchell Starc starred as Australia took control of the day-night first Test in Brisbane.
[NEXT_CONCEPT]
Police have confirmed that a body found on a Fife beach was that of a missing 43-year-old woman.
[NEXT_CONCEPT]
Italy wing Leonardo Sarto has agreed to join Glasgow Warriors on a two-year contract in the summer from Zebre.