...is a post incident review with support people involved, and their management teams, along with directors and executive involvement to identify what the problem was that caused the business to be inoperative for the duration of the incident, what policies and procedures need to be followed going forwards, and so on. Once policies are established, solutions that support those policies can be implemented.
As an example for your situation, since a vendor was involved in an upgrade, that should have been part of a scheduled change. The change should be documented ahead of time as to what is being done, what systems are going to be touched, and who the responsible parties both within the company and external to the company are for that change. Included in the documentation should be the fallback plan for dealing with issues that crop up during and after the change, within an appropriate test window that is included in the change window, as well as clearly defined backout procedures. "fix and fall forward" or equivalent statements are not, and should not be, considered acceptable plans. Wherever possible you want to have documentation attached that the procedures involved have been tested in a suitable test environment. (This may not be possible in situations where a test environment would cost as much to prepare as the production environment.)
As far as limiting remote access, as others have pointed out, such limits are trivial based on what type of remote access is in place, and what policies are established. At the very least account authorizations required for performing changes on production devices should require someone in house approve that authentication, be specific to the time when those changes are scheduled to happen, and should not allow similar access to devices or types of devices not involved in the change.