The Icelandic international completed his protracted switch to White Hart Lane this week, having at one stage looked odds-on for a move to Merseyside. Spurs paid Hoffenheim a fee of around £8m for the 22-year-old's services.
Rodgers, who worked with Sigurdsson at Reading and during a loan spell at Swansea last season, admitted he had held talks with the player about a transfer to Anfield, but said he was not willing to pay over the odds in order to secure a deal.
"I was quite relaxed about it," said the Reds boss. "Gylfi did fantastic for me at Swansea last season. I brought him in from Hoffenheim, where he wasn't playing, and he did very well. He scored 7 goals in 19 games, which was very good.
"He and I both sat and spoke. I believed playing football was going to be the most important aspect for him, but obviously it was important financially as well.
"We agreed a deal for him to go to Swansea, and that was wrapped up. I then became Liverpool manager, so that (Swansea move) was not going to happen. He then had a choice of where he wanted to go.
"I knew what the market was, and I wasn't prepared to pay anything over what I had known was agreed already."
Rodgers admitted he was disappointed to miss out on a player who would have added goals and dynamism to his midfield, but insists the club will now pursue other transfer targets.