Typing the value of matrix elements in matrix plot

Question

I want to type the value of matrix elements when plotting it on the topside of the bar.

Example: $$M=\left(\begin{matrix} 0.77 & 0.04 & 0.01 & 0.0\\ 0.04 & 0.81 & 0.0 & 0.0\\ 0.02 & 0.0 & 0.81 & 0.08\\ 0.0 & 0.07 & 0.04 & 0.93 \end{matrix}\right)$$

the output:

my code:

exp1 = ( {
   {0.77, 0.04, 0.01, 0.0},
   {0.04, 0.81, 0.0, 0.0},
   {0.02, 0.0, 0.81, 0.08},
   {0.0, 0.07, 0.04, 0.93}
  } )
data = ArrayPad[Abs[exp1], {0, 1}];
DATAAA1 = 
 ListPlot3D[data, Mesh -> Full, InterpolationOrder -> 0, 
  Filling -> Bottom, FillingStyle -> {Opacity[0.7]}, 
  ColorFunction -> "IslandColors", PlotRange -> All, 
  BoxRatios -> {1, 1, 1}, DataRange -> All, ImageSize -> 600, 
  PlotTheme -> "Monochrome", 
  PlotStyle -> Directive[Opacity[0.9], Blue], 
  AxesLabel -> {Text[Rotate["Input", -10 Degree]], 
    Text[Rotate["Output", 60 Degree]], 
    Text[Rotate["Probability", 100 Degree]]}, 
  LabelStyle -> Directive[Black, Thick, 12], Boxed -> False]

the result i have:

Edit

There are complicated solutions that manually construct a Graphics3D object, but can there be a simple solution using standard functions?

Edit 2

I found a manual solution using the following latex code

\documentclass[]{article}
\usepackage{lipsum}
\usepackage{pgfplots}
\pgfplotsset{compat=1.15}
\usepackage[a4paper, total={17cm, 25cm}]{geometry}
\begin{document}
\begin{figure}\centering
    \setlength{\unitlength}{0.085mm}
    \begin{picture}(800,250)\linethickness{0.3mm}
        \includegraphics[width=5cm,height=5cm]{sample.eps}
        \put(-490,380){\scriptsize$0.77$}
        \put(-350,410){\scriptsize$0.81$}
        \put(-220,430){\scriptsize$0.81$}
        \put(-90,490){\scriptsize$0.93$}
    \end{picture}
\end{figure}
\end{document}

the output:

but I am still searching for an automated way on Mathematica to solve the problem.