Dean Hammond, Craig Mackail-Smith and Wayne Bridge were the goalscorers who propelled the Seagulls to ninth in the npower Championship, three points off the play-offs.
It was an impressive response to their previous outing when they were beaten 3-1 at home by fellow play-off hopefuls Watford.
Poyet knows they have a good chance to finish in the top six and said: "I don't know if we'll go up but if we don't make the top six, it will be a shame.
"We've got an absolutely incredible opportunity and if we don't make it, we won't have anyone to blame apart from ourselves.
"This was a much-needed win.
"A few weeks ago we had 27 shots, 17 of them on target, and only scored one goal.
"In this game we hit the target three times and scored three goals.
"Is that normal? No. But that's football and that's what can happen in this division. Ipswich have been very good lately."
- Sports & Recreation
- Wayne Bridge