The Villans had conceded 15 and scored none in their previous three games and Wayne Routledge added to their woes as he fired the hosts ahead in the ninth minute. But Villa had looked set to take the points when Andreas Weimann levelled just before the interval and Christian Benteke scored from the spot before Graham struck.
He said: "It is a huge point although we should have seen it through. But it's a massive point and we were very good and threatening in the second half."
He added: "In the first half they were coming at us from all angles and we had to weather that storm and we needed a couple of good saves from Brad and they also hit the woodwork.
"But to get the goal before half-time certainly helped us and it had a galvanising effect, it gives you something to get going and in the second half we were very good.
"We have been beaten heavily in the last three games so this is a huge point for the future of the club.
"The young lads in the side have been excellent and when you get beaten heavily you learn a lot about people and today showed they are mentally strong."
Swansea manager Michael Laudrup, meanwhile, was left scratching his head as to how his side had not won a game in which they had almost 70 per cent possession and had threatened to run away with during an opening half-hour when Villa were all at sea.
Michu, Graham and Routledge were among those to miss gilt-edged chances, and the Dane said: "We did not win because we only scored one goal from seven chances with that first-half performance.
"It was a great performance - it could have been 4-0 after 12 minutes - but we know how it is when you don't take chances."
Source: PA
Source: PA