Is it too much cement under my crown on implant?

I would recommend you schedule a follow up appointment with your dentist to asses the cementation and your ability to clean around the implant. Residual cement not cleaned from the margins of the crown can lead to implant failure. 

An implant crown should not fall off if well designed.  It should rely on friction. The cement seals.  In your case, the new "permanent" cement may not show in an xray. Yout dentist may need to get you numb to clean the excess cement. It is very important as it can irritate and hurt the bone surrounding the implant.

Go back and have her check what the problem is..... Cement under a crown over an implant can jeopardize the long term health of the implant including loss of the implant. I use a technique where the crown is cemented outside the mouth and the crown and abutment are one piece and fabricated by a CEREC machine.

I highly recommend you go back to your dentist and have him/her check your implant.  An x-ray may even be of value, as it could show the fit and any excess cement around the gums.The pinch you felt when cementing the implant could be normal.  Oftentimes the gums rebound, pressing against the abutment and the crown pushes the gums back away as it is cemented back into place.  The important thing here is that the gums got pushed away, and did not get stuck under the crown.  Sometimes the gums push so closely against the implant that we have to use the gum laser to open up the area for the crown so that it can go back into place properly.Another important thing is the dentist making sure to remove any excess cement that might be irritating the gums.  Again, this is easy to detect by your dentist.