WindowElements -> {"StatusArea"}

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

WindowElements -> {"StatusArea"}

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

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"}]