City ended a run of four games without victory, the last time they scored six goals in a league match was against Sheffield Wednesday at Filbert Street in January 1987.
David Nugent scored twice in the first 18 minutes - the first from the penalty spot - and Lloyd Dyer, Anthony Knockaert, Martyn Waghorn and substitute Marko Futacs also got on the scoresheet.
"You hope if you turn in the performances you put in a result like that," Shakespeare said. "Over the course of the season I think some of the football and attacking play has been outstanding. But we have, in all honesty, missed the chances. There is no getting away from that.
"But today, as in any game, it was very important to get the first goal. When we got that it seemed to settle everyone down a bit.
"Then, to go and score the amount we did and share the goals around, I thought we were very, very professional today from start to finish. It was a very accomplished performance.
"I have worked with Lloyd Dyer since he was a young boy at West Brom and I think that in the last few weeks he has been playing the best football of his career.
"He has got that one thing that defenders are frightened of - pace. And it caused Ipswich a lot of problems. It was a good dressing room to be in afterwards but it is only one game. But we have done well and it bodes well."