Sam Allardyce's side have been hampered by the absence of their record signing, who has yet to feature since joining from Liverpool permanently in the summer.
It has left the Hammers devoid of attacking options, and they have managed just 14 shots on target in the Premier League this season. By contrast, Spurs had 29 shots against Cardiff alone.
The east Londoners head to White Hart Lane on Sunday without a win in eight away league games, failing to score in their last four, but Villas-Boas is not taking them lightly.
"They are still a very objective and aggressive team," he said of Carroll's absence.
"They are very direct and we know what to expect against them.
"We will have to be alert at set plays, crosses into the box and make the play very, very strong.
"We were successful against them last season, winning home and away, and we are highly motivated for the game against West Ham.
"A London derby is always difficult, so it will be an extremely difficult match."
Tottenham head into the game boosted by the news that captain Michael Dawson has signed a new three-year deal at White Hart Lane.
The 29-year-old has made 293 appearances for Spurs since joining in January 2005 and is set to start against West Ham on Sunday.
Few could have expected such a turnaround for Dawson after Villas-Boas' openness to selling the Yorkshire-born defender last year.
The Portuguese later admitted that was a mistake and will hope for a similarly positive reaction from Emmanuel Adebayor.
Spurs tried to sell the Togo striker during the summer transfer window, only to be scuppered by the player's refusal to leave.
"I think his motivation will be high," Villas-Boas said of Adebayor.
"At the moment we have found extreme comfort in playing one striker rather than two like last season.
"What Ade will give us is that possibility, that link-up play he does so well with somebody else. At the moment we continue to play with one striker. We scored so many goals and we don't suffer, so it looks like the way forward for us.
"All three of them will be in competition for that place."