Ancelotti's men have beaten Chelsea, Leicester, Arsenal and Sheffield United in their last four Premier League outings, keeping three clean sheets in the process.
The most recent of the 14 goals top-scorer Calvert-Lewin has netted in all competitions for the club this term came just prior to that sequence, in the 1-1 draw at Burnley on December 5.
Ahead of the New Year's Day home clash with West Ham, Ancelotti hailed the 23-year-old England international's contribution.
"It is true that he didn't score in the last (few games) as usual, as he did at the beginning, but it is also true that he was really important," Ancelotti said.
"Against Chelsea (he won) the penalty, against Arsenal he was involved in the first goal that was an own-goal, he had an opportunity against Sheffield United.
"He is still working really hard, so I don't have to ask more."
Everton head into 2021 lying fourth in the top flight, four points behind leaders and champions Liverpool, who have played a game more.
The Toffees began the season with four successive victories, then took maximum points only once in seven games before embarking on the current winning streak.
"We found solidity at the back, after a difficult month of November, and we are pleased," said Ancelotti, whose time in the job reached a year earlier this month.
"We know that we can compete, we have improved our confidence and our belief and we are ready to be tested again against West Ham.
"I think we are doing well. We improve, compared to last season (when they finished 12th), and this is the target, to improve every year."
When asked about the difference between the first run of four wins - which included beating West Brom 5-2 and Brighton 4-2 - and the current one, Ancelotti said: "I think we didn't change our style, our philosophy, but sometimes in some games we changed the strategy.
"The fact this squad is able to adapt to the different situations... One is we were good I think to adapt to the fact we lost important players.
"Second, there are teams that, if you concede (space on the) pitch, you have more difficulties. So in some games, our block was a little bit deeper than normal, and we got for this reason good results.
"The fact we are able to adapt is a good sign for the squad."
For the encounter with 10th-placed West Ham - and former boss David Moyes - Everton have Richarlison back available after he missed the Boxing Day win at Sheffield United under concussion protocol, but James Rodriguez (calf) remains sidelined.
While Lucas Digne is not yet ready to return to action, pictures of the full-back doing individual training appeared on Everton's official Twitter feed on Thursday along with the words "working his way back to full fitness".
On Wednesday Ancelotti had said of the Frenchman, who had ankle surgery in late November: "We have good news on Lucas Digne, that he is starting individual sessions and maybe in one week, 10 days, he will be able to train with the team."
Just before Digne underwent surgery, Ancelotti had spoken about the prospect of him being out for "two or three months".
Everton were scheduled to host Manchester City on Monday but the fixture was postponed due to positive coronavirus cases at City.
The Government's announcement on Wednesday that the Liverpool City Region was moving into Tier 3 means Friday's game at Goodison Park will now have to be played behind closed doors, having previously had up to 2,000 fans permitted.
Register for free to continue reading
Registration is a free and easy way to support our truly independent journalism
By registering, you will also enjoy limited access to Premium articles, exclusive newsletters, commenting, and virtual events with our leading journalists
Already have an account? sign in
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies