He was outclassed by Windu in lightsaber combat and was scrambling. But he was not scared because Anakin had arrived. It is explained in the Revenge of the Sith novelization.
DARK SIDE FRIDAY - Did you know Palpatine feared Qui-Gon Jinn? Palpatine was immensely powerful and he could see the future which made him very confident about pretty much anyone who stood against him. So why Qui-Gon Jinn?
Windu didn't beat Palpatine because he was stronger and more skilled in lightsaber combat - he beat him because of three major reasons: (1) his unique lightsaber style, (2) his Shatterpoint technique, and (3) he got lucky.
Palpatine's face was left disfigured after fighting Mace Windu, but despite Star Wars' medical technology, he never tried to heal his scars. In Star Wars: Revenge of the Sith, it was revealed that Emperor Palpatine's face wasn't just the product of old age but also scarring from fighting the Jedi.
It's implied that this isn't feigning and Palpatine is actually fighting to win. In the book its implied that he allows Mace to move him and make certain moves, however this is a not uncommon dueling tactic, waiting for openings and surprising an opponent.
Giving in to his feelings, Anakin cuts off Mace Windu's hand, giving Palpatine the opportunity to kill him. Anakin regrets this almost instantly, but the thought of Padme was stronger than his remorse This is the moment Anakin officially became Darth Vader and led to serious issues in the Skywalker Saga.
Mace completely dismisses him as not just the Chosen One but also a Jedi. He seems particularly spiteful towards Ahsoka, especially when the last time the two interacted, he brushes off as a citizen. Then, he blantantly admits to not trust Anakin.
Though the Clone Wars were all but over, the Jedi were in terrible danger. Anakin revealed to Mace that the Sith Lord sought by the Jedi since the fight with Darth Maul was none other than Palpatine himself.
Sidious himself felt that he and his peers had outgrown the use of lightsabers, and only continued carrying them to mock the Jedi. He ultimately viewed his own lightsabers as little more than an affectation, and rarely wielded them in combat.
Yes, Sidious did let Windu beat him
The number one reason why many Star Wars fans believe that Darth Sidious did let Mace Windu defeat him is that it was the perfect way to finalise Anakin's turn to the Dark Side.
What Would Happen To The Galactic Republic? With Chancellor Palpatine's death, the de facto "Prime Minister" of the Republic, the Senate would be left without a leader and there would be considerable political confusion and chaos. There would be a need to elect a new chancellor to lead the democratic government.
Jedi Masters Mace Windu, Kit Fisto, Saesee Tiin, and Agen Kolar confronted Chancellor Palpatine upon learning of his secret identity as a Sith Lord.
In the fictional Star Wars universe, Mace Windu is portrayed as a Jedi Master who sits on the High Council during the final years of the Galactic Republic. He is notable for wielding a unique purple-bladed lightsaber, and is regarded as one of the most powerful Jedi of his time, second only to Yoda.
Jedi Master Yoda is the most powerful of them all. This should come as no surprise, as he was the head of the Jedi Order in the prequels and was revered for his abilities during the original trilogy. Yoda's power is unmatched and was a real threat to Darth Vader and the Imperials.
Tarkin was the embodiment of Palpatine's desire to rule by fear and was put in charge of the Death Star project. In many ways, Tarkin was more ruthless than Palpatine.
First on the list of Palpatine's rivals is Darth Bane. He was not only unrivaled with a lightsaber in his day, but he was also a master at shrugging off the force powers of others, Sith and Jedi alike. As the sole surviving Sith of the Jedi-Sith War, his knowledge of the force should not be underestimated.
She may have not been a powerful Jedi warrior, but few can say Jocasta Nu didn't play a vital role in Star Wars history, showing just why she scared Emperor Palpatine so much.
Dooku voluntarily left the light side behind and became Darth Sidious' dark side disciple, taking the secret name Darth Tyranus and leading the Separatist army. Dooku advanced Sidious's secret plot to take over the galaxy, but forgot that betrayal is the nature of the Sith.
Amedda was one of the few beings in the galaxy who knew Palpatine's secrets, most notably his true identity as a Sith Lord.
Mission to Mathas. Padawan Windu was trained in the ways of the Force by Jedi Master Cyslin Myr. Following his early trials as a youngling, Windu attained the status of Padawan by becoming Jedi Master Cyslin Myr's apprentice.
Apart from Depa Billaba, Mace Windu has had four other known apprentices in Legends: a human female named Devan For'deschel, a human male named Echuu Shen-Jon, a human male named Darrus Jeht (though this was informal), and an unidentified human male who failed as an apprentice (and may not even be within the Legends ...
because his Padawan Ahsoka. never became a knight. She left the order when she was still a padawan. This is why Anakin was denied the rank of master.
In the final days of the Clone Wars, Windu turned to Kolar again, calling on him, Saesee Tiin and Kit Fisto to arrest Supreme Chancellor Palpatine. Confronted by the Jedi, Palpatine threw off his guise and revealed himself as Darth Sidious.
You know, the reason Mace Windu told Anakin to wait in the Council Chambers is because when he got back from killing Darth Sidious, Mace Windu planned on granting Anakin the rank of master. Yep. It's sad but true.