`WindowElements -> {"StatusArea"}`

    CreatePalette[
     PasteButton[  Style[StatusArea["\[Gamma]", "esc-g-esc"], 
                         FontFamily -> "Courier", 12], 
                   RawBoxes["\[Gamma]"], ImageSize -> {30, 20}], 
     WindowStatusArea -> ":)", 
     WindowElements -> {"StatusArea"}]

![enter image description here][1]

Full answer:

    CreatePalette[
     Table[With[{i = i},
       Annotation[Button[Row[{"Label ", i}], Print[i]], "Yeah, " <> ToString[i], "Mouse"]
       ],
      {i, 10}],
     WindowStatusArea -> Dynamic[MouseAnnotation[":("]], 
     WindowElements -> {"StatusArea"}]


  [1]: https://i.sstatic.net/Xmz4E.png