The Wolves stopper and his team-mates are still smarting from their 2-0 defeat by Finland in Cardiff back in March, when their chances of qualifying from Group Four were ended.
Hennessey, who should earn his 22nd and 23rd caps against Finland and Liechtenstein in Vaduz on Wednesday, said: "These two games are still massive for us, we need to get the points to make the group table a lot better than it is now.
"We have to prove we can beat Finland after what happened in March against them in Cardiff.
"I suppose it is a revenge mission. We were so disappointed by that result and the way we played that revenge is not too strong a word.
"Third place would be brilliant - we would improve our seeding in the next competition. We have to make that our goal."
Anglesey-born Hennessey has dreams of overtaking Neville Southall's 92-cap Wales record.
He said: "I am only 22, I want a lot more caps. Neville Southall's record number of caps for Wales is a target, obviously. It is the sort of total that only really goalkeepers can achieve.
"I hope I can take his record. He was fantastic, and achieved so much, so to get anywhere near him would be a proud achievement for me.
"I'm enjoying the Premier League now Wolves have been promoted and I feel that having played for Wales has been a great help for me.
"I have been facing big teams and big players, and a lot of them do play in the Premier League, so my Wales experience has come in very helpful.
"Hopefully I have a long career ahead of me for Wales and we will qualify for a finals in my time, definitely. Why not? Just like at Wolves, we are all young and we will all improve."
Hennessey's Wolves club-mate David Edwards, shares the lingering annoyance at that Finland defeat in March.
He said: "We need six points now to make this campaign a successful one, third place is important and achievable.
"It is a goal we want to reach and it is something we can manage over the next week.
"The home defeat by Finland in March was the real low point for us in this group, we had a chance of qualifying up until that point. But we were beaten by a more experienced side, and it showed.
"It wrecked our momentum. It was not a good game and they were better that us all over the pitch."
He added: "It was a real shame and we have a big point to prove in Helsinki. We know we were poor and they were technically good and we really need to get into their faces.
"We must work extremely hard, like all Welsh teams should do, and stop them playing. We have power, pace and running power in our team and we must make use of that.
"It is a shame that we have lost Jack Collison and Joe Ledley through injury, but we have others who can come into the side.
"They had the edge over us in Cardiff with their experience, they made us look very ordinary. So we have to use our fitness and strength to really get about them."