Robert and Christianne Shepherd, aged six and seven, of Horbury, West Yorkshire, died from carbon monoxide poisoning in October 2006.
Neil Shepherd told Wakefield Coroners' Court he was "paralysed by guilt" over their deaths.
He sobbed as he described his "perfect son" and "feisty, loving" daughter.
The children were staying at the Louis Corcyra Beach Hotel with their father and stepmother when they complained of feeling unwell, the inquest heard.
They were found dead the following day by a maid and Mr and Mrs Shepherd were found in a coma.
Post-mortem tests revealed carbon monoxide levels in Robert and Christianne's bloodstreams were 56.8 and 60.7% respectively - levels above 50% are fatal.
An inspection of the boiler found it had been incorrectly installed and a safety cut-off device had been deliberately short-circuited.
Mr Shepherd said: "I firmly believe my children would be here today if Thomas Cook had carried out an inspection of those boilers."
The father of two children who died on holiday in Corfu said he "firmly believed" they would be alive had Thomas Cook inspected a faulty boiler.