Ancelotti was pleased with the overall performance and the return to form of his strikers but suggested that confidence cannot yet be taken for granted in a side enduring its worst run for almost 15 years.
"There were differences in the first 30 minutes of this game and the other 60," added Ancelotti.
"We were a bit worried, less confident in that first period. When we scored the first goal, everything was okay.
"With this victory, our confidence will improve, but we have to wait to say everything is OK."
He was equally circumspect in his assessment of Sturridge, who turned in his second excellent display in four days after scoring five times for the reserves on Thursday.
Ancelotti praised the former Manchester City player but stopped short of suggesting the forward would retain his place in the side.
"He deserved to play," said the former AC Milan boss. "He played well, scored, and is a good player and a good striker, very dangerous.
"In the future, he'll have opportunities. We have a lot of games in this period coming up.
"I think he has to fight with the other strikers but everyone has to fight. There are a lot of players in competition up front."
Ipswich caretaker manager Ian McParland, who took the helm for the visitors following the departure of Roy Keane on Friday, conceded that a week of upheaval at Portman Road had done little to help his side.
"The boys are a bit shell-shocked, with the manager going," conceded McParland.
"For half an hour, we were doing okay, we were in the game but we gave them three bad goals.
"I've never been beaten like that. It hurts my pride but I'll bounce back. Let's not forget who the lads were playing against.
"Some Premier League clubs were beaten seven or eight here last year, so maybe we're in good company."
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