According to statement from the ICC, Dilshan and Jayawardena were found to have breached Article 2.1.5 of the ICC Code of Conduct for Players and Player Support Personnel, which relates to "excessive appealing during an international match".
The charges were laid by on-field umpires Bruce Oxenford and Rod Tucker, as well as third umpire Ian Gould and fourth umpire Steve Davis.
Dilshan and Jayawardena were charged for excessive and prolonged appealing in a keenly-contested low-scoring match that New Zealand won by one-wicket last night.
"Irrespective of the outcome of an umpire's decision, players are not entitled to prolonged appeals as these can be construed as pressuring the umpires. Both the players accepted their mistake and apologised for their actions," Pycroft later said.
All Level 1 breaches carry a minimum penalty of an official reprimand and a maximum penalty of 50 per cent of a player's match fee.
