Ignoring errors in Trigger

I have a stored procedure which is called inside a trigger on Insert/Update/Delete.

The problem is that there is a certain code block inside this SP which is not critical. Hence I want to ignore any erros arising from this code block.

I inserted this code block inside a TRY CATCH block. But to my surprise I got the following error:

The current transaction cannot be committed and cannot support operations that write to the log file. Roll back the transaction.

Then I tried using SAVE & ROLLBACK TRANSACTION along with TRY CATCH, that too failed with the following error:

The current transaction cannot be committed and cannot be rolled back to a savepoint. Roll back the entire transaction.

My server version is: Microsoft SQL Server 2008 (SP2) - 10.0.4279.0 (X64)

Sample DDL:

IF OBJECT_ID('TestTrigger') IS NOT NULL
    DROP TRIGGER TestTrigger
GO
IF OBJECT_ID('TestProcedure') IS NOT NULL
    DROP PROCEDURE TestProcedure
GO
IF OBJECT_ID('TestTable') IS NOT NULL
    DROP TABLE TestTable
GO

CREATE TABLE TestTable (Data VARCHAR(20))
GO

CREATE PROC TestProcedure       
AS      
BEGIN 

    SAVE TRANSACTION Fallback
    BEGIN TRY
        DECLARE @a INT = 1/0
    END TRY
    BEGIN CATCH
        ROLLBACK TRANSACTION Fallback
    END CATCH
END
GO

CREATE TRIGGER TestTrigger
ON TestTable
FOR INSERT, UPDATE, DELETE 
AS
BEGIN
    EXEC TestProcedure   
END
GO

Code to replicate the error:

BEGIN TRANSACTION
INSERT INTO TestTable VALUES('data')
IF @@ERROR > 0
    ROLLBACK TRANSACTION
ELSE
    COMMIT TRANSACTION
GO