convert rgb to cmyk problem

The automatic conversion from RGB ( no idea what tag you used ) to CMYK is to blame for inaccurate color, especially on screen.  What I would typically do is print a proof ( on the appropriate paper ) of the RGB colors ( while still in RGB mode ).  Then I use a Pantone swatch book that has been printed using a similar paper ( Pantone Solid Color Guide ). Once you determine each of your RGB colors' closest solid color cousin, you can then refer to Pantone's Solid to CMYK equivalent(s).  As stated already, you may not be able to match your RGB's exactly, but you can get pretty close through trial and error.  You essentially are or will be creating a custom color palette.  You did not mention how your RGB's will ultimately be used, so we have to assume they will be printed.  Final output will play an additional role in determining color accuracy.  paper also plays a role.  Viewing color on your monitor will only frustrate you.  Start over with a new CMYK document and avoid any automated conversions.

Goran,

There is a decisive difference in the colour gamuts.

There is no way to create CMYK colours that are that are within the RGB gamut but outside the CMYK gamut. This applies to (some of) the brightest RGB colours.

While it is impossible to get such actual RGB colours in CMYK, you may be able to make acceptable changes to alternative colours that appear less dull/dirty

While you still work in RGB Color Mode, you can try the following, taken from here,

https://helpx.adobe.com/illustrator/using/adjusting-colors.html

Shift an out-of-gamut color to a printable color

Some colors in the RGB and HSB color models, such as neon colors, cannot be printed, because they have no equivalents in the CMYK model. If you select an out-of-gamut color, an alert triangle appears in the Color panel or Color Picker.

• Click the triangle to shift to the closest CMYK equivalent (which is displayed in a small box by the triangle).

Then you can try to adjust the colour.

You can see more about colour gamut here (and many other places), also with a direct comparison,

https://en.wikipedia.org/wiki/Gamut

https://en.wikipedia.org/wiki/RGB_color_spaces#/media/File:CIE1931xy_gamut_comparison.svg