The increase in oil prices, caused by the war in Ukraine and the Covid-19 pandemic, will be passed on to consumers, Walsh told the BBC.
He also criticised Heathrow, saying the airport should have "prepared better" to avoid recent disruption. The airport said Walsh’s comments were "ill-informed".
"Flying will be more expensive for consumers, without doubt", he told the BBC Sunday Morning programme, adding the "high price of oil" will be "reflected in higher ticket prices".
He urged airports which "cannot cope" to adjust their schedules now, so they can accommodate as many passengers as possible.