However, Quinton Fortune's stunning late goal - his first for Doncaster - denied the visitors and left Keane bemoaning his side's defensive frailties.
"I think we gave bad goals away," said the Irishman.
"You always think if you score three goals away from home you're going to win the game and in terms of going forward this was our most encouraging display.
"I certainly think we had the better of the chances and when you are 3-2 up with five or 10 minutes to go you would hope you can see the game out.
"But that's the way it's going for us at the moment."
Keane insists his side must continue to work hard if they are to turn around their dismal run of form.
He added: "It's certainly going to be one of those seasons where it's going to be a long, tough battle for us and we're going to have to give some players the benefit of the doubt as they settle into the football club both on and off the pitch.
"We've got one or two injuries and we're lacking a bit of confidence as you would expect, but no-one is going to hand us a victory. We've got to keep battling away and do it for ourselves."
Keane did manage to crack a smile when he was asked if he had seen Fortune score any goals similar to his equaliser during their time together at Manchester United.
"He bloody didn't no," joked Keane. "Not even in training.
"Don't worry, I'll be seeing him in a minute!"
While Keane was able to take heart from aspects of his side's performance, opposite number Sean O'Driscoll was disgusted with his side's display.
Despite seeing Rovers lead for much of the game, O'Driscoll said: "I thought it was a poor performance.
"We didn't get out of first gear and we haven't played like that for a long time.
You can talk about the goals we scored, but they hide a multitude of sins.
"We pride ourselves on our level of performance and I didn't think it was anywhere near what we are capable of.
"I thought we lacked ideas and didn't do a lot of things that we've done well week in, week out."
O'Driscoll, like Keane, was also disappointed with his side's defensive display.
"We didn't mark the thrower on the first goal. Our line for the free-kick (for Ipswich's second goal) was poor and we didn't challenge for the third goal," he added.
"There's not much they can do about Quinton Fortune's strike, and if they had scored that sort of goal against us you would have to hold your hands up.
"But they (Ipswich's three goals) are the sort you can't concede in this division."