Back when USSR was dismantled, it was replaced by the Commonwealth of Independent States, a sort of Union, like the EU, where Russia and its allies used to maintain good relations with each other.
The NATO and the EU (almost the same thing) started to phagocytize countries of this CIS.
Russia is right.
Sorry, but that makes no sense. None whatsoever.
For starters, what do you mean by "to phagocytize"? I am pretty certain that those countries were not invaded by NATO or anything.
Also, I think that you are either misrepresenting or misremembering things. There are currently nine CIS members (thanks to Wikipedia for the list).
Country Signed Ratified Charter ratified Membership Status
Armenia 1991-12-21 1992-02-18 1994-03-16 official member
Azerbaijan 1991-12-21 1993-09-24 1993-12-14 official member
Belarus 1991-12-08 1991-12-10 1994-01-18 official member
Kazakhstan 1991-12-21 1991-12-23 1994-04-20 official member
Kyrgyzstan 1991-12-21 1992-03-06 1994-04-12 official member
Moldova 1991-12-21 1994-04-08 1994-06-27 official member
Russia 1991-12-08 1991-12-12 1993-07-20 official member
Tajikistan 1991-12-21 1993-06-26 1993-08-04 official member
Uzbekistan 1991-12-21 1992-04-01 1994-02-09 official member
The only former member is Georgia. Turkmenistan was never a full member, but that seems to make little difference in practice (it is considered a founding member and an associate state). Ukraine, too used to be a founding member without full membership until 2014.
Georgia applied for NATO membership in 2004 and left the CIS in 2008-2009. It is still not a NATO member, and it has been partially occupied by Russia since 2008. There are literally no countries that used to be members of the CIS and have already joined NATO, although odds are that Georgia and Ukraine will at some point.
There are also no CIS members of any kind (former or current, founding or associate) that are currently members of the EU either. There are several EU members who joined since 1999 that used to be part of the Soviet sphere of influence, yes. Feel free to explain why they are not within their rights.
How would that give Russia - which is currently a true imperialistic state if any ever existed - any justification in invading Krimea, and now Ukraine?