Former Wigan boss Martinez replaced David Moyes at Goodison Park and went back to his old club to sign James McCarthy on deadline day, with loan deals for Gareth Barry and Romelu Lukaku also completed before the window shut.
Those deals followed earlier moves for Arouna Kone, Antolin Alcaraz, Joel Robles and Gerard Deulofeu with Allardyce, who revealed West Ham had failed with a bid for Lukaku, left praising Everton's business.
"Gareth Barry in particular is an outstanding acquisition from Manchester City and with Romelu Lukaku joining their frontline as well he's given them some excellent options," he said.
"They've got a very good variety of players added to the ones that were already there.
"Arouna Kone has been bought in and they've only really lost Marouane Fellaini so not only is their starting XI strong but their whole squad is now very strong."
Everton picked up their first league win under Martinez against Chelsea last week and remain unbeaten after three successive draws preceded the 1-0 victory.
Allardyce is aware that Martinez will be looking to stamp his own style on the Everton squad and is not expecting an easy ride at Upton Park on Saturday.
"Our job on Saturday is to make sure we know what we're playing against," he added.
"They will try and pass the ball out from the back more than they did under David Moyes but after that they generally play the same as they did under David.
"They had a fantastic result against Chelsea last weekend so we're expecting a tough match on Saturday."
The Hammers have struggled to find the back of the net of late and have not scored in the Premier League since their opening day win over Cardiff.
Midfielder Mohamed Diame has targeted victory against Everton as West Ham strive to add much-needed goals to their impressive defensive displays.
"It will be a good game, Everton did well against Chelsea, they are a good side but we are at home so we need the victory," he said.
"You can see we are strong defensively at the moment, Sunday's clean sheet was our third in four games, and we need to keep going like that.
"At the other end we need to try to score goals, it's obvious to say but we need to score goals to win the game."
Diame was brought to English football by Martinez, who signed him from Rayo Vallecano during his time at Wigan.
The Senegal international is looking forward to facing his former manager and has backed Martinez to be a success on Merseyside.
"I am looking forward to coming up against my old boss Roberto Martinez on Saturday," Diame added.
"I will always have a lot of respect for him because he brought me to the Premier League.
"He has good ideas in football and I'm sure he will do a good job at Everton.
"I know a few of their players too, because I played with some of them at Wigan - if a manager has done well with players it's normal that he will bring them with him."
- Sports & Recreation
- Marouane Fellaini
- Romelu Lukaku
- David Moyes
- Gareth Barry
- Arouna Kone
- Barclays Premier League
- Manchester United