Problem upgrading to version 4.1

Dear Sir or Madam – whoever may be kind enough to help,

I tried to upgrade to version 4.1 the other day, and it failed; the browser appeared to get stuck – nothing happening, so I closed the browser and on trying to login again afterwards I got the message:

Fatal error: Call to undefined function wp_json_encode() in /websites/123reg/LinuxPackage21/je/mb/ow/jembowdenwatercolour.co.uk/public_html/wp-admin/includes/misc.php on line 668

I googled the issue which led me to the following thread on the support forum, and carefully read through it all. It appears that others have had the same problem:

https://wordpress.org/support/topic/fatal-error-after-41-upgrade

It is the first time I’ve had any kind of ‘crash’ with WordPress, so I decided to follow the suggestion you can see here from Ross Mitchell first
(“The function “wp_json_encode” is defined in “wp-includes/functions.php” so maybe just replace it from the v4.1 zip file.”)
I tried this first instead of the one from James Huff, as it sounded simpler.
I found it worked, in that I am now able to get back into my Admin area and work as usual. However, I am aware that I have just replaced one file with a new one (from version 4.1) and I have a message inside my dashboard telling me that
“An automated WordPress update has failed to complete – please attempt the update again now.”.

Please can you recommend a course of action for me next? I am worried that I will encounter the same problem as last time if I just click to attempt upgrade again.
(Please bear with me – I am not very ‘techie’, and am having to take ages over all of this as I am learning at every stage. Have spent most of today over this issue!)

Many thanks in advance.
Jem