Kevin Davies grabbed an equaliser for the League One promotion chasers just three minutes after David McGoldrick had given in-form Ipswich a 38th-minute lead.
A 1-1 draw was no more than Preston deserved with Town boss Mick McCarthy blaming himself for his side's poor display after making seven changes.
Grayson said: "We definitely deserved the draw at the very least. We controlled large periods of the first half, played good football, and then showed resilience and good attributes when we went a goal behind.
"I told my players to test themselves against a Championship team and see how far they can go, and my players stood up to it.
"We passed the ball around well, had some really good chances and my keeper Declan Rudd only had one save to make at the end.
"We would have taken a draw before the start of the game but I am disappointed we didn't go on and win it."
Preston shaded the first half with Luke Chambers clearing an Iain Hume header off the line before Ipswich, themselves in a rich vein of form in the Championship, took the lead.
Paul Huntingdon inexplicably handled Carlos Edwards' corner and McGoldrick scored at the second attempt, after his spot kick was initially saved by Norwich City loanee Rudd.
But the visitors hit back and Hume was again denied, this time by onrushing Town keeper Scott Loach, before Preston restored parity.
Davies looked yards offside when he collected Lee Holmes' through ball, but the veteran striker was played on by a stricken Tyrone Mings and continued to calmly slot the ball past Loach.
Preston were full value for that equaliser before the second half levelled out and a dismal game headed predictably towards a replay.
Chances were few and far between with Paul Gallagher wasting a good opening for the visitors before Ipswich rallied near the end and McGoldrick almost snatched an unlikely victory only to see Rudd save to his close-range effort.
Town boss McCarthy had little complaints in his post-match summing up, saying: "We were poor, as poor as we have been all season.
"But that was credit to Preston, who you have to congratulate for not letting us play. I thought they played well and deserved a replay.
"But I also take responsibility. I picked a team with too many players who had not played enough. They were not battle-hardened or match-hardened.
"I wanted to avoid a replay and give players a rest. But now we have to travel up there - so that didn't work, did it?"