Ms Skripal, 33, and former Russian spy Sergei Skripal, 66, were exposed to the Novichok agent on 4 March in Salisbury.
They were both admitted to Salisbury District Hospital along with Detective Sergeant Nick Bailey.
She said she hopes to return to her home country “in the longer term”, but does not want assistance from the Russian Embassy.
Ms Skripal said she was “shocked” to wake up from a coma 20 days later and discover they had been poisoned.
“I still find it difficult to come to terms with the fact that both of us were attacked,” she said.
“We are so lucky to have both survived this attempted assassination.
“Our recovery has been slow and extremely painful. The fact that a nerve agent was used to do this is shocking.”
Ms Skripal described her treatment as “invasive, painful and depressing”.
She said she was “grateful to all of the wonderful, kind staff at Salisbury Hospital”.
“I also think fondly of those who helped us on the street on the day of the attack,” she said.
Ms Skripal gave a statement to press yesterday at a location in London. She asked for privacy for herself and her father.
“We need time to recover and come to terms with everything that has happened,” she said.
Ms Skripal continued: “I was discharged from hospital on the 9th of April and continue to progress with treatment, but my life has been turned upside down as I try to come to terms with the devastating changes thrust upon me both physically and emotionally.
“I take one day at a time and want to help care for my dad till his full recovery.
“In the longer term I hope to return home to my country.
“I’m grateful for the offers of assistance from the Russian Embassy, but at the moment I do not wish to avail myself of their services.”
Prime Minister Theresa May has said it is “highly likely” Moscow was behind the attack, but Russia has denied involvement in the incident.
Russian president Vladimir Putin wished Mr Skripal “good health”, but suggested he would have “died on the spot” if Novichok had been used.
Moscow’s ambassador to the UK, Alexander Yakovenko, has demanded the right to see the Skripals, claiming the UK was flouting international law by refusing consular access.
He highlighted the 1963 Vienna Convention, which gives consular officials access rights if one of their nationals is in prison, custody or detention. Mr Yakovenko said: “We are saying that they are isolated because we don’t have access to them.
“This is our interpretation. You can call it detained, you can call it isolated, you can call it kidnap.
“Unless we see them it is difficult to make a conclusion.”
Mr Yakovenko had acknowledged the Foreign Office told him they did not interpret the situation in the same way and added: “I got the impression that we will never see them.”
Scotland Yard has said it will not discuss “any protective or security arrangements” put in place for the Skripals.
Detectives from the UK’s Counter Terrorism Policing network continue to investigate the attempted murder.