Frank Lampard was also on target as the reigning champions carried on from where they had left off last season when they clinched the title with an 8-0 victory over Wigan.
Related ArticlesChelsea 6 West Brom 0Bullish Ancelotti predicts more successChelsea complete £17m Ramires moveAncelotti on Chelsea's title defenceChelsea: Premier League 2010-11 season previewSantos 'to report Chelsea over Neymar deal'Ancelotti had expressed concern his side were not ready for the campaign following the Community Shield defeat to main rivals Manchester United the previous weekend.
And preparations were not helped by reports the Chelsea players were locked in a dispute with the club's hierarchy over planned changes to bonus payments.
But the comprehensive victory over West Brom banished concerns the champions could lose ground in the opening weeks.
Ramires, the £17 million capture from Benfica, is set to start at Wigan next week and, with Ancelotti insisting the players who appeared in the World Cup are still short of full fitness, the manager believes there is more to come.
"This is a message for us, not the other teams," Ancelotti said. "We had a difficult pre-season and now everything is OK. But it was nothing special. We did our job.
"We knew we could have a problem when we gave the players who had been at the World Cup 26 days' holidays but they needed the recovery. We knew they couldn't play in the first game of pre-season.
"Ashley Cole, Frank Lampard, John Terry can improve their condition," the Italian manager added in a reference to his England trio. "In the next two weeks they will be 100 per cent."
As for the issue of bonus payments, Ancelotti said: "I didn't speak to the players about that. I'm not interested, that is between the players and the owner.
"I don't think they are unhappy. I have watched the way they play. They are very happy."
Drogba rounded off last season with a hat-trick against Wigan and repeated the feat although Ancelotti was anxious to praise the contribution of all his strikers.
"Didier Drogba did a fantastic job," he said. "He worked very hard for the team as did Florent Malouda and Nicolas Anelka. It's very important to have this commitment from our strikers.
"I don't know if he's the best striker in the world. He scored a lot of goals last season and he can do the same this season. He is a fantastic striker and I'm just glad he is with us."
West Brom manager Roberto di Matteo endured a painful return to the club he served as a player and conceded his side must improve quickly if they are to avoid immediately dropping back into the Championship.
"We were playing the champions on the first day so we knew it was going to be tough although the score line was probably harsh on us," Di Matteo said.
"But not too many teams will come away from Stamford Bridge with anything.
"We have to be sure we don't give away easy goals. We know we have to learn and we have to learn quickly. And we have to improve quickly. On the other hand we don't have to play Chelsea every week."