Gregor McKinley, prosecuting, said:
Sotheby's has given Tate Modern a verbal estimate of pre-damage value of approximately between £5 million to just over £9 million.
The work required to restore this picture will be complex and lengthy.
Complications to this work include the unique painting technique used by the artist and the fact the ink used by Mr Umaniec has permeated the paint layers and the canvas itself.
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.