Despite being relegated after going into administration, Grant has still managed to guide Portsmouth to the FA Cup Final.
O'Neill thinks that is a huge achievement and he said: "It has been exceptionally difficult for Avram Grant and the managers before would have found the whole situation particularly difficult.
"It is a situation where I think he must come out of it with great credit.
"To have reached the Cup Final is a terrific achievement against all the odds.
"He has said himself that he felt that the club's fate was sealed when they were docked the points. That probably knocked the heart out of them. So he has kept their spirits up tremendously well."
Villa have had their own cup success this season - reaching the Carling Cup Final and the FA Cup semi-final.
While they were beaten in both by Manchester United and Chelsea respectively, O'Neill still feels that this season has been a positive one and shows that there is a bright future at Villa Park.
But to ensure that they do not end a season of promise without any reward, O'Neill is desperate to see his side clinch a place in Europe next term.
Champions League qualification now looks a long shot but a place in the Europa League is in their sights.
O'Neill, who has set his side the daunting task of winning their last five games, added: "If we qualify for Europe for the third consecutive year why shouldn't I be happy? That is what people aspire to.
"There are domestically three competitions you can win - the Premiership, the FA Cup and the Carling Cup.
"We have contested the final in one and the semi-final in the other and when the league table was formed after three games we haven't been out of
the top seven.
"I've been absolutely delighted with the team and the effort that they put into the game.
"Their performance against Everton on Wednesday epitomised it just a few days after putting in a big, big effort at Wembley against Chelsea.
"We have had a couple of disappointments recently and we have to fight against that all the time.
"But there is great resilience and great character in the side and more than that the team can play.
"There are one or two players who could help make the difference. Of course, everyone is looking for those extra players that make the difference. Teams all around Europe can say the same.
"But I think the Villa team is very close and very young with tons of ability and can improve even further.
"There is plenty of confidence in team and there is still something to go for.
"It is a tall order to win the last five games but that is our intention and there is no room for any let-up.
"To accumulate 70 points in a season would be quite phenomenal but we are a long way off that target with 55 points on the board.
"There are still five games to go. It is not easy for us but still worth going for -starting at Portsmouth."