"While this is not the 'hole-in-one' we hoped for, there is always risk with breaking new ground," said Thomas Zurbuchen, associate administrator for NASA's science mission directorate, in a statement.
"I'm confident we have the right team working this, and we will persevere toward a solution to ensure future success."
The drill hole is the first step of a sampling process that is expected to take about 11 days, with the aim of looking for signs of ancient microbial life that may have been preserved in ancient lakebed deposits.
Scientists also hope to better understand Martian geology.
The mission took off from Florida a little over a year ago and Perseverance, which is the size of a large family car, landed on 18 February in the Jezero Crater.
Scientists believe the crater contained a deep lake 3.5 billion years ago, where the conditions may have been able to support extraterrestrial life.
NASA plans a mission to bring around 30 samples back to Earth in the 2030s, to be analysed by instruments that are much more sophisticated than those that can be brought to Mars at present.