Contribution Payable Under Which Act?
Are you referring to contributions payable under ESI or EPF? If you have missed the contributions for March and April, pay them now and wait for the notices regarding interest and damages. When they arrive, pay those as well. If ensuring timely payment of these contributions is your responsibility, then I would suggest that the interest and damages should be charged to you, and the employer might impose a fine for your significant oversight.
No HR or Accounts person should forget the dates for remitting statutory contributions and submitting returns. If they fail to pay and file the returns on time, they should bear the consequences.