The Icelandic international impressed Rodgers when working under him at Reading and has now linked up with the Swans on loan from Hoffenheim.
Sigurdsson cancelled out Marc-Antoine's opener with his first goal for the club and then laid on the winner for Danny Graham.
Rodgers said: "I put him in the team when I was manager at Reading so I know everything about him.
"I felt we needed an offensive midfielder for the second half of the season and he fits the bill perfectly for that.
"He did not need persuading to come here. He knows how I work and when I went into Reading he was a wonderful young talent.
"If I see that talent, I will put them in the team - and he went on that season and scored 20 odd goals.
"He is one I've always kept in contact with and I just felt this would be a terrific club and he has fitted in perfectly."
Rodgers added: "It has been difficult for him at Hoffenheim because he's had three different managers there.
"He is a very clever guy, loves British football and knows how I work."
Rodgers is delighted Swansea have started to pick up points away from home as they followed up last month's win at Aston Villa.
He said: "We could have scored four or five. We are a little club fighting to earn respect at this level through our game.
"It is not our mentality and philosophy to sit back. There is an inherent belief in our game.
"We know we needed to improve our away record and we've had a couple of good results."
In contrast, Albion continue to struggle to win at home - just two this season - and they have managed only eight points at the Hawthorns compared to 18 on their travels.
He said: "It was an all too familiar story, I'm afraid. We keep giving ourselves a chance with good away results, getting into good situations.
"Then when we come to play in front of our home crowd, we disappoint them by not being able to get a result.
"It is a vicious circle which can only be broken by us getting a result and we don't seem capable of doing it."
Hodgson added: "When we took the lead I thought maybe this was going to be a situation where we would get a result.
"But the lead only lasted a minute and then you find yourself suddenly 2-1 down and it's a familiar pattern.
"Once again we will go home disappointed and dissatisfied and very downhearted.
"We all get down when we lose and up when we win. That's football."