Mr Tillerson said in Mexico City that "two strong sovereign countries - from time to time - will have differences."
Relations between the neighbours are at their lowest point for decades.
A US plan, unveiled this week, to expel to Mexico all illegal immigrants found crossing the US border regardless of nationality has angered Mexicans most.
Mr Videgaray said at a joint news conference: "There`s a concern among Mexicans, there`s irritation [about] what has been perceived as policies that might be harmful for the Mexicans and for the Mexican industry."
Media captionRepublican Senators have faced angry crowds at town hall meetings across the country.
In his own statement afterwards, Mr Tillerson said: "There`s no mistaking that the rule of law matters along both sides of our border."
Homeland Security Secretary John Kelly, who joined Mr Tillerson for the closed-door meetings in Mexico City, emphasised there would be no mass deportations or use of military force in US immigration operations.
"Everything we do in [the Department of Homeland Security] will be done legally and according to human rights and the legal justice system of the United States," he said.
Speaking to a group of US chief executives at the White House earlier on Thursday, President Donald Trump acknowledged the Mexico visit would be a "tough trip".
"We`re getting really bad dudes out of this country at a rate that nobody`s ever seen before", Mr Trump said.
The Trump administration issued a new policy on Tuesday targeting millions of illegal immigrants for possible deportation, mirroring a previous executive order signed by the president.
The new policy, which seeks to step up enforcement of existing US immigration laws, subjects nearly all illegal immigrants to deportation and speeds up their removal.
It also calls for sending back to Mexico immigrants caught crossing the border illegally, irrespective of where they are from, and deporting anyone charged or convicted for any crime.
Mr Tillerson and Mr Kelly will probably also face questions about the new guidelines in their meeting with Mexican President Enrique Pena Nieto.
President Trump has insisted that Mexico will pay billions for a wall along the US border, which prompted Mr Nieto to cancel a planned Washington visit late last month.
Both US and Mexican officials made no mention of Mr Trump`s proposed wall at the news conference on Thursday.
Mr Trump has also ordered a report, due on Friday, listing all foreign aid the US provides to Mexico.
It is unclear why he requested the review, but its inclusion in Mr Trump`s executive order on constructing a wall along the southern border suggests he may use it for leverage in negotiations with Mexico.
Mexican officials are also concerned about Mr Trump`s pledge to renegotiate trade partnerships between the two countries.
The president has proposed to levy a 20% tax on Mexican imports to pay for a border wall.
Democratic senators urged Mr Tillerson and Mr Kelly to work through tensions with their Mexican counterparts on Thursday.
"We urge you to use your visit to disavow vitriolic rhetoric and forge a strong partnership based on mutual respect with the government of Mexico," the senators wrote in an open letter.
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