"We still need to win a third of our games, but this was a massive result for us and a deserved one too," said Ternent, who was pleased to see his team gain revenge for a 6-1 drubbing they received at Ipswich in October.
Ipswich boss Joe Royle, whose side had not lost away since September, said: "We were abysmal in the first half but credit to Burnley. They are much better than their position suggests and need not have any worries about relegation."
Glen Little and David May put Burnley firmly in the driving seat before England Under-21 international Richard Chaplow put his team three up with an outstanding right-foot volley on the hour.
Ipswich, very much second-best, suddenly found new life through substitute Martijn Reuser, who helped himself to a couple of well taken goals to set up a frantic finish.
Matt Richards hit a post as Burnley threatened to cave in, but Ternent's men kept their nerve for Robbie Blake to make the game safe in injury time with his 18th goal of the season.
"We never do things simply here and there are parts of our game that need to improve," added Ternent.
"But the way the lads are having a go is very pleasing and it could have been a lot more comfortable had we been awarded the penalty we should have had when Glen was fouled with the score at 3-0.
"It was nervous at the end, but no-one could deny us our right to the win."