Gregor McKinley, prosecuting, said:
Mr McKinley said work to restore the painting will take about 20 months and cost "something around £200,000."
Gareth Morgan, defending, said it would take a "significant amount of effort, expert effort at that" to restore the "important, valuable piece of art".
Paintings by Russian-born artist Rothko often fetch tens of millions of pounds.
Judge Roger Chapple, at Inner London Crown Court, told Umaniec: "Your actions on the 7th of October of this year were entirely deliberate, planned and intentional."
He said it was "abundantly clear" that Umaniec was "plainly an intelligent man" and told the court he had described Rothko as a "great painter" in a letter he had written to him.
The judge also said the incident had led to galleries reviewing security arrangements at a cost to themselves and the taxpayer.
"The effects of such security reviews is to distance the public from the works of art they come to enjoy," he said.
A man has been arrested over the defacing of a Mark Rothko painting at the Tate Modern.
A 26-year-old man was arrested by Sussex Police at an address in Worthing.
He's been arrested on suspicion of criminal damage and is now in custody at a Sussex police station.
Art restorer Amy Griffin, from the Simon Gillespie Conservation Studio, says that it should be possible to remove the graffiti without damaging the original painting.
The Assistant Editor of the Art Review magazine, Oliver Basciano, says there's a long history of artworks being defaced for political and so-called "artistic" reasons.
A man has admitted defacing a Mark Rothko canvas at the Tate Modern worth tens of millions of pounds. Eyewitnesses said the man wrote some words with a black pen on one corner of the 1958 work "Black on Maroon".
Paul Brand has the latest.
Police are hunting for a vandal who walked into the Tate Modern art gallery and defaced a valuable painting by Mark Rothko.
The visitor daubed black paint on "Black on Maroon" during a visit to the gallery yesterday afternoon.
Eyewitness Tim Wright posted on Twitter:
"This guy calmly walked up, took out a marker pen and tagged it. Surreal. We gave a description to the gallery. Very bizarre, he sat there for a while then just went for it and made a quick exit."
Earlier this year, Rothko's Orange, red, yellow was sold for £53.8 million - the highest price ever paid for a piece of post-war art at auction.
The 1961 painting went under the hammer at Christie's in New York.