So, his denial of the fact that he wasn't Obi-Wan's failure per se, made it easier for him to let go of those small hidden emotional connections and bring him again to his full potential.
Update: So apparently Hayden Christensen said in the Q&A yesterday in Toronto that there will always be a little bit of Anakin in Vader, and that line was Anakin trying to absolve Obi-Wan of guilt.
Obi-Wan Did Not Fail Anakin
Anakin himself made a series of wrong decisions and took a series of steps that led him to the dark side and two decades of service to Emperor Palpatine as his apprentice.
I have failed you. Anakin Skywalker : I should have known the Jedi were plotting to take over! Obi-Wan : Anakin, Chancellor Palpatine is evil!
Anakin Hated Obi-Wan Because of an Imagined Relationship With Padme. Although that couldn't have been further from the truth, Anakin apparently built up a scenario in his mind, which was only heightened by the Jedi Council's obfuscation in other areas.
In Episode III, just before they are to set off on their respective missions, Obi-Wan and Anakin share a farewell. Anakin admits to Obi-Wan that he has been arrogant and unappreciative of his training, and apologizes to his master.
Yes, when Darth Vader turned back to Anakin Skywalker and sacrifice himself to save his son, he dies and Obi-Wan uses the force to connect with Anakin's spirit. In that time Anakin apologizes to Obi-Wan, desperately asking him to forgive him for everything he has done to him and everybody over the years.
David Porter provides some great philosophical context to why Obi-Wan would not regret leaving Anakin alive, as it was obviously “the will of the Force” that Obi-Wan be unable to finish him off, and “the will of the Force” that Anakin live on to kill Sidious himself in the future.
He had a softish spot for a handful of individuals and unlike many other Sith, Vader didn't generally kill innocent people for no reason - but he always hated the Jedi and he had no regrets about what happened to them. The best proof of this is how he throws himself into becoming the Empire's primary Jedi hunter.
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.
But Obi-Wan Kenobi's finale helped make Ben's case. After defeating Darth Vader in the Obi-Wan Kenobi finale, Obi-Wan broke down and began tearing up when he saw Anakin's scars. It was the first time he had seen Anakin's face since leaving him to burn on Mustafar, and so he apologized for everything that had happened.
But in a strange moment of comfort, Darth Vader took much of the weight off Obi-Wan's shoulders. He told him, “I'm not your failure, Obi-Wan. You didn't kill Anakin Skywalker. I did.” We saw later in the original trilogy, on some level Ben still believed he bore some responsibility.
“I'm not your failure, Obi-Wan,” Vader says. “You didn't kill Anakin Skywalker. I did.” This allows Obi-Wan to finally let go of all his guilt over Anakin's transformation into Darth Vader.
If you are asking about Vader post-Mustafar, then no, she doesn't. Padmé doesn't seem to know Obi-wan cut off his limbs and left him to burn alive, Obi-wan didn't believe Anakin to be alive and Anakin's surgeries were still happening as Padmé died so there was no way for her to know.
The added risk Darth Vader takes in allowing children to live in a situation where he could have killed them proves that he regrets killing Younglings and will avoid harming any more children for the rest of his days, though intense intimidation is a dark strategy to avoid repeating his Youngling massacre.
Many have taken to the Internet to suggest that if it was really killing Kenobi that Vader was after, he simply could have brushed away the fire that followed to thwart his escape. And that is true. However, Vader is not just looking to kill Kenobi. He wants to make him suffer.
Theory 1: Leia Doesn't Remember Ben Is Obi-Wan
Throughout her encounters with Kenobi in the series, he refers to himself as Ben. The most straightforward explanation would be that Leia knows the person who rescued her is Ben, and never connected the dots that Ben is actually Obi-Wan.
He does. Right at the end. With Luke crying over him and Vader sensing his anguish and pain he had inflicted on all those who had cared for him.
She also knows Obi-Wan, and she knows him well. Her holographic plea for help, already iconic, will never be the same. She knows Obi-Wan's real name as well as his alias of “Ben.” When Luke comes barging into her cell and says, “I'm here with Ben Kenobi,” Leia jumps off the bunk in an instant.
In the material around the film from the Legends timeline, it's established that by the end of Star Wars: Episode III - Revenge of the Sith, Kenobi was one of the characters who knew Anakin's Sith name was Darth Vader. However, what he didn't know was that he was still alive after Mustafar.
"You Were Right About Me. Tell Your Sister You Were Right." — Anakin Skywalker.