O'Neill quit the Villa Park hot-seat on the eve of the season and neither caretaker manager Kevin McDonald nor the Northern Irishman's permanent successor Gerard Houllier have managed to achieve consistently good results with a highly-talented squad.
He said: "They are one of the great under-achievers this year. Martin O'Neill is one of the top managers in this country and for someone to take over from Martin was always going to be difficult. They are big shoes to fill."
Pulis added: "And with Gerard Houllier being out of the game for a while it was always going to be a slow transition and it has taken them a bit of time to get going.
"I am sure they will be better next year, they are a great football club. There are clubs that are at a level above us at the moment and Villa are one of them but we will try to go there and win."
Pulis certainly cannot be accused of failing to get the maximum out of his squad after watching them secure a place in the FA Cup final for the first time in the club's history last weekend.
The 5-0 thrashing of Bolton at Wembley represented the highlight in a season in which Stoke have enhanced their reputation as a growing force in the top flight.
But Welshman Pulis is demanding his players put the Wembley showpiece against Manchester City on May 14 to one side and focus on finishing the season strongly.
"Winning the Bolton game was fantastic and the way we did it was the icing on the cake but you move on," he said. "We have seven massive games left, it was a semi-final, not a final, we play a great club in Manchester City, a club which has invested enormous sums but we have to move on.
"We have an important game against Villa and then an important week - we play Wolves on Tuesday and then go to Blackpool on Saturday. We gave the players a couple of days off but they were in yesterday and they were brilliant, they trained really well."
Source: PA
Source: PA