Mayor Bill de Blasio said on “Morning Joe” Monday that he believes implanting universal pre-K is the key component in improving the city’s school system—and he insisted he is not in a feud with Gov. Andrew Cuomo.

“The whole educational structure, every piece of it matters,” de Blasio said. “I have to worry about 1.1 million kids a year, and by the way, only 70,000 kids go to charters.”

“Morning Joe’s” Mika Brzezinski pressed the mayor on his reported contentious relationship with both Cuomo and Success Academy’s Eva Moskowitz. Showing a clip of de Blasio on the campaign trail attacking Moskowitz, Brzezinski asked if his disagreement with Moskowitz is “personal,” a charge with de Blasio denied.

“We all accept that charters have something to teach us and we can learn something from them,” de Blasio said.

The Success Academy is expected to file a lawsuit on Monday against de Blasio to overturn his decision to prevent co-locations of three of their schools. Success officials are also filing a lawsuit against state Education Commissioner John King to reverse City Hall’s decision against the other co-locations.

Meanwhile, Public Advocate Letitia James said she will sue to shut down all charter schools that are co-located, and ask a judge to get rid of the admissions lottery for the 2014-15 school year.

On “Morning Joe,” De Blasio also defended his tax hike plan, saying that he is open to other alternatives from Albany, but he said he needs “verification” that universal pre-K will be funded.

“I think a dedicated tax is the best way,” de Blasio said. “I’m absolutely open to an alternative that gets the job done.”

De Blasio also touted his plan for free after-school programs for middle school students, saying it will double the current service levels.

De Blasio and Brzezinski also touched upon teacher retention, which both agreed is another issue that needs to be addressed. De Blasio agreed to come back sometime and discuss teacher retention for 20 minutes.

Joe Scarborough also asked about Liam Neeson’s tour on Sunday of the carriage horse stables, saying “don’t cross this guy, he will kill terrorists on a cross-Atlantic flight.”

“I am a Liam Neeson fan,” de Blasio said. But, he said “horses in the city in the streets today don’t make sense.”