You have yourself a classic case of DIY. The middle is easy... but that other stuff goes and buggers it all up.
There are a few option, most of which aren't fantastic.
Filler will work but it will look like a big section of filler. It never really works on bigger areas to blend seeing as one solid lump of soil color is almost as obvious as the misscut.
Trying to plug it with flooring material to lessen the hole and then fill it is a slightly better plan, its not easy to get that kind of stuff cut in there but it is possible.
I can't really tell how big that hole is, looks about 1/2 - 3/4 inch... you could remove the last 6 or so inches of the door casing and install plinth blocks to cover it and carry your q.round into the door frame. This is the best of the worst ideas as it can almost make it look on purpose.
The best thing to do is just remove those pieces, undercut the door and try again. Sometimes the amount of work involved makes filler look like not such a bad idea. Remove the q.round, pull the transition and the pieces and voila.