Houllier is pleased with the solid base and promising squad O'Neill has left at his disposal after twice narrowly missing out on securing a Champions League spot.
Now Houllier will try to take Villa to the next level once he has tied up the loose ends with the French Football Federation where he worked as technical director.
Caretaker-boss Kevin MacDonald will take charge of Monday's clash at Stoke which Houllier will watch on television in his homeland.
Houllier said: "Several times I thought Martin would succeed me at Liverpool.
"All I know is that he a great manager and brought up a good squad at Aston Villa. This is one of the reasons we have a good base to work from.
"It is difficult to succeed to him - but it is always difficult to succeed to anybody. When it is difficult, it is exciting.
"I trust the squad, I trust the players, I believe there is potential here to do something well.
"I know that Martin was nearly there. One player left (James Milner) but another one came (Stephen Ireland) who is quite skilful too.
"We will do our best to achieve what we want and more. It will take time but we know that.
"My philosophy is progress, performance, and pleasure."
Houllier will eventually look to strengthen the squad further although he hinted the January transfer window is not the ideal time for big changes.
He said: "We know at some stage we need to improve the team gradually.
"But I don't think January is always a good period because you don't get the best (players) but we'll prepare for the future.
"I am quite happy with the squad. When people say Aston Villa is a good club, they also add that they have got good players.
"They must have because they finished in a Europa League position (sixth)."
MacDonald will be at the helm for a sixth successive match against Stoke.
He has rejected the chance to be part of Houllier's first team coaching set-up and will revert to his role as reserve team coach.
MacDonald will have to check on the fitness of Ireland before finalising his side.
The former Manchester City player suffered a hamstring injury during the warm-up against Everton in Villa's last match a fortnight ago.