More than 150 flights were canceled at airports on Wednesday.
Most customers will have been given advance notice of the cancellation, although airlines including EasyJet and Tui made it.
There were long lines at the terminals.
The transport secretary said airlines and operators were struggling with staff shortages and had oversold flights.
At least 31 flights have been canceled by EasyJet to destinations including Bologna, Barcelona, Prague, Krakow and Edinburgh.
The airline said last week that it would be cancelling around 24 flights a day from the airport.
Around 34,000 travellers have been affected by the cancellation of six daily flights by Tui Airways at Manchester Airport.
The company said all customers had been contacted, but some people said their flight had vanished and they had not heard from the company.
The airline said that some of the short-haul flights were pre-planned and passengers were told in advance.
The vast majority of flights would operate as scheduled, according to Airlines UK, which represents the major British airlines.
Two million people are going to fly over the next few days, with the Jubilee bank holiday coming on the same day as half-term.
Mr Shapps said that the government had made it clear that it was up to industry leaders to deal with travel disruption.
Michael Turner, a nurse from Shoreham, is trying again to go on a holiday with his family.
Mr Turner was told his EasyJet flight had been canceled 20 minutes before he was due to leave.
He rebooked a flight from Manchester Airport which was all that was available and he said he experienced chaos in the departure lounge.
Mr Turner said they spent three hours waiting to be escorted off the plane to collect their luggage.
They were put on a coach without being told where they were going and then waited to be taken back to the airport for a flight.
The transport secretary said he would meet with airports, airlines and ground handler to find out what went wrong and how they would end the current run of delays.
Despite government warnings, operators oversold flights and holidays. This must not happen again and all efforts should be made to prevent a repeat of this in the summer.
The government was accused of being missing in action.
Louise Haigh called on ministers to take responsibility for tackling the disruption by addressing the security checks for new staff and working with industry to addresschronic low-pay.
The aviation industry laid off thousands of workers during the Pandemic when international travel was halted, and it's difficult to find replacements.
Since Covid, airports and airlines across Britain have cut thousands of jobs.
The PC Agency's chief executive, Paul Charles, argued that the government was to blame for the chaos since demand for flights returned after the Pandemic.
The transport secretary has got a bit of a nerve, he said.
Without certainty over when travel restrictions would be lifted, the industry was not able to recruit more staff.
Kelly Sandhu, from the Aviation Recruitment Network, said the process of hiring new workers took a long time so there was not a quick fix.
The vast majority of flights this week would operate as scheduled despite the fact that the sector had only a few weeks to recover and prepare for one of the busiest summers in recent years.
The final Covid restrictions were lifted on March 18.
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