The survey of 810 pilots was commissioned by the British Airline Pilots Association (Balpa). It shows that 39% found their abilities were compromised by tiredness at least once a month.
A further 14% said this happened about once a week. However, only 51% said a decision not to fly because of fatigue would be supported by their chief executive.
Meanwhile, only 49% of respondents said they were given enough time in simulators to improve their manual handling skills while 51% said they were confident pilots were adequately trained to recover their aircraft manually following a high-altitude emergency.
UK pilots currently have two four-hour sessions in a flight simulator every six months but the time is dominated by handling emergencies while taking off and landing and low-altitude flying in poor visibility.
The CAA said: “Pilots undergo continuous training and development, especially in relation to the manual recovery from unusual situations.”
Laser pens are also proving to be a problem, with 55% of respondents to the survey saying they had experienced an attack within the last year. A further 4% had suffered six or more.
While CAA figures show reports of lasers being shone at aircraft has risen from 746 in 2009 to 1,442 in 2014, the actual true figure may be higher. The Balpa survey revealed the CAA was notified of fewer than two-thirds of incidents.
Balpa general secretary Jim McAuslan said: “Shining a laser into a cockpit can temporarily blind the pilots, often for some time, putting the aircraft and its passengers at needless risk.
“We believe all but the lowest-powered lasers should be strongly regulated, and treated as offensive weapons.”