UK angry at 'unacceptably high' Channel migrant numbers
Patel made her comments on social media the day after British border officials detained 235 migrants as they tried to cross the narrow stretch of water between the UK and France - a daily record high.
The government has come under increasing political pressure from critics to tackle the issue and has floated the idea of using the Royal Navy to patrol the Channel.
"The number of illegal small boat crossings is appalling and unacceptably high. The figures are shameful," Patel said in a series of messages on Twitter.
Patel, whose parents left Uganda in the 1960s to live in Britain, called on "genuine refugees" to claim asylum in European Union states rather than travel to the UK.
And she urged the French authorities to do more.
"We also need the cooperation of the French to intercept boats and return migrants back to France," she wrote.
Among those criticising the minister has been Brexit Party leader Nigel Farage, who has long campaigned on immigration issues and has accused the government of "talk and no action".
During the 2016 referendum in which Britain voted to leave the European Union, Brexit supporters argued for the UK to "take back control" of its borders over fears too many migrants were arriving.
Last month the interior ministers of France and Britain signed an agreement to create a new joint police intelligence unit to combat migrant traffickers and reduce the number of illegal Channel crossings.
Media reports claim that more than 3,400 people have made the crossing so far this year.
In 2019, 2,758 migrants were rescued by the French and British authorities while trying to make the crossing - four times more than in 2018, according to French officials.