The Blues went some way to lifting the gloom at Stamford Bridge as they began their defence of the trophy they have won for the past two seasons in emphatic fashion.
The managerless visitors proved ideal cannon fodder for Ancelotti's faltering double winners, who had won just one of their previous nine league games to all but surrender the championship.
Making a point: Carlo Ancelotti believes there is some way to go before his side can claim to be out of their slump
The Chelsea boss, who has twice been given votes of confidence by billionaire owner Roman Abramovich in the past fortnight, said: 'We needed to have this kind of performance.
'The result was good and we did a lot of things well in this game - the performance of the team, the strikers scoring again. We don't have to be excited. But, obviously, with this victory, our confidence will improve. We have to wait to say everything is okay.'
Ancelotti's decision to continue last season's policy of fielding some youngsters in the early rounds of the cup did not backfire, with Daniel Sturridge and Frank Lampard scoring twice, Salomon Kalou also finding the net and Nicolas Anelka ending the goal drought that has coincided with Chelsea's two months of misery.
Chelsea toiled for the opening half-hour but once Kalou found the net, the floodgates opened.
Not feeling so Blue now: Chelsea smashed six past a hapless Ipswich side at Stamford Bridge
'There were differences in the first 30 minutes of this game and the other 60,' Ancelotti said. 'We were a bit worried, less confident in that first period. When we scored the first goal, everything was okay. But we have to play more games to say the bad moment has gone.'
Friday saw Ancelotti laugh off a lone protest calling for his head and today proved the Italian still had the backing of the vast majority of Chelsea fans, who chanted his name towards the end.
'It's very nice, obviously, to hear the fans like that,' he said. 'We all have to be close, and the fans showed fantastic support today.'
Despite some good performances from his young players, especially two-goal Sturridge, Ancelotti was unwilling to guarantee them a place in his side against Blackburn next weekend.
Dan the man: Blues striker Daniel Sturridge notched a brace in the romp
He said of Sturridge, who also netted five times for the reserves on Thursday: 'He deserved to play. He played well, scored, 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.'
Van Aanholt limped off with 20 minutes remaining and Ancelotti revealed the youngster had suffered a minor hamstring tear.
The main injury today, however, was inflicted on Ipswich, who looked a side in disarray following Roy Keane's sacking this week. Caretaker boss Ian McParland admitted the visitors were given 'a right thrashing'.
'I knew what was going to happen today,' he said. 'The boys are a bit shellshocked with the manager going.'
McParland believes Keane may have fared better had he still been in charge, saying: 'I'd like to think it would have made a difference.
'For half an hour, we were doing okay. We were in the game. 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 beat seven or eight here last year, so maybe we're in good company.'
McParland was praying Keane's replacement would take charge in time for Wednesday night's Carling Cup semi-final first leg against Arsenal, with Paul Jewell a strong favourite to land the role.
'I think he's got a really tough job,' he said. 'I hope he's in by Wednesday!'
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