Try the following (added parenthesis around the countrycode clause):
INSERT INTO [AntronERP_DB].[dbo].[tblCountry](countryCode,countryName,secCode,stdCountryCode)
(SELECT [CountryCode],[CountryName],[Sector],[CountryCode] FROM [ANTRONMASTERDB].[dbo].[CountryMaster]
WHERE Sector IS NOT NULL AND (CountryCode <> 'UK' OR CountryCode <> 'LK' OR CountryCode <> 'US') )