"We have been brought up in a background of terrorist activities," Jayawardene told reporters after the players returned home.
"We are used to hearing, seeing these things – firing, bombings. So we ducked under our seats when the firing began. It was like natural instinct," he was quoted as saying by a cricket website.
Sri Lanka has seen civil war with Tamil Tiger rebels who are fighting for a separate homeland. The Sri Lanka cricketers were on their way to the Gaddafi stadium to play third day of the second and final Test when their bus was attacked by at least a dozen armed terrorists.
Six players were injured in the incident while eight others, most of them security personnel, were killed. Jayawardene felt the attack on the team could have happened anywhere and should not blacklist Pakistan.
"We were not aware of security lapses. It's an unfortunate incident. In hindsight, this could have happened anywhere in the world," he said.
"In the future, I think all of us will step back and look at the bigger picture besides just touring abroad, taking into account our families," added.
He said the players just wanted to spend time with their families now. "I am a Buddhist and I think we have done some merit in our previous birth to escape with minor injuries."
Lankan players arrive home after Lahore attack
Sri Lanka's cricketers were reunited with their families after returning home early on Wednesday following an attack by gunmen in Lahore.
The players were welcomed home to Bandaranaike International Airport by friends and families, cricket officials, sports minister Gamini Lokuge and a large media contingent.
Around a dozen gunmen attacked the team's bus on Tuesday with rifles, grenades and rockets, wounding six players and a British assistant coach and killing at least eight Pakistanis.
"It's great to be back in Sri Lanka with our families and loved ones," Sri Lanka captain Mahela Jayawardene said after the team's arrival home at 3.20am (2120 GMT).
"We are still shocked by what has happened but we are relieved that no one in the team suffered more serious injuries or were killed," he added.
Five players and assistant coach Paul Farbrace were transported straight to Nawaloka hospital in central Colombo for checks on their injuries.
The most seriously injured player was Thilan Samaraweera, who was shot in the leg. Doctors will decide on Wednesday whether to try to remove the bullet.
Early reports suggest he would be unable to play cricket for between six to eight weeks.
Tharanga Paranavitana, a 26-year-old playing his first international tour, was the next most seriously injured after being shot in the chest. The bullet, which narrowly missed his heart, was later removed by Pakistan doctors.
"I am fine now," Paranavitana said at the airport. "I feel very lucky."
The other players injured, all of whom suffered minor shrapnel wounds, included Jayawardene (ankle), Kumar Sangakkara (shoulder), Ajantha Mendis (head) and Suranga Lakmal (leg).
Jayawardene was the only player not sent to hospital on the team's return.
Sangakkara paid tribute to the team's bus driver, Mohammad Khalil, for saving lives.
"The truth is that we owe our lives to Khalil for the courage he showed in getting the bus going again after the initial attack and into the stadium," Sangakkara said.
"After the first shots the bus had come to a halt on the roundabout and we were sitting ducks for the terrorists, but he got us out of there just in time."