Town are still without a win in 12 Championship games and fell behind inside seven minutes when Craig Beattie netted for the Welshmen.
However, Pablo Counago - who rejected a summer move to the Swans - netted an equaliser eight minutes later to take a point.
Keane said: "We're making progress and this gives us something to build on.
"It's certainly not doom and gloom.
"The players are training well and I can't fault them, but we just can't seem to put the ball in the back of the net.
"We had good chances in the second half and should have won the game.
"It wasn't ideal to concede another early goal.
"I'm not sure if the boy was offside but you have to deal with setbacks in a game.
"You haven't got a divine right to score first.
"Swansea keep the ball well.
"They have got good players but we had the better chances and I don't think we looked like a side at the bottom of the table."
Eyebrows were raised before the game when Keane handed new loan goalkeeper Asmir Begovic his debut and left usual number one Richard Wright out of his 18.
"It's my job to make decisions and I like to surprise people sometimes," said the Irishman.
"It's good for players to recharge their batteries and chill out for one or two days.
"But I know Richard and I know his reaction to being left out will be first class."
Swansea made a dream start as Angel Rangel played a long ball forward and summer signing Beattie burst into the box, under pressure from Gareth McAuley and Tommy Smith.
Despite the tight angle out wide on the right he managed to get the better of both defenders and squeeze a powerful shot past Begovic.
Town equalised when Counago and Jaime Peters combined brilliantly on the right of Swansea's area.
They played a slick one-two and, after Peters fed the Spaniard, he coolly slipped the ball past goalkeeper Dorus de Vries.
Ipswich had the better chances after the break and went close
through Counago, Jon Walters and Connor Wickham.
Swansea boss Paulo Sousa said: "Ipswich belong at the top, not the bottom, and they have got some very good players here.
"For that reason, I'm happy with one point although I'm always happier when we win.
"In the first half we controlled the game better and could have scored more goals.
"We had more possession but in the second half we weren't as direct as I would have liked.
"Sometimes you need to risk a bit more and be a bit more direct.
"We have to attack space quicker and attack different areas of the box, but overall I was very proud and happy with the result.
"Ipswich are having a difficult time and you have to have a great personality to come to a place like this.
"I'm a winner and I like my players to have a winning mentality."