Renowned for their slick passing football, the Welsh side had to dig in and show different qualities following Taylor's red card for a high tackle on Lewis McGugan after only 53 seconds of the npower Championship play-off semi final first leg.
"I'm very proud of my players, they were absolutely outstanding," said Rodgers. "We knew it was going to be an emotional game but to lose a man so early was incredible."
He added: "I thought our shape was outstanding. We kept our shape and I felt sorry for Stephen Dobbie as he was looking forward to playing here but we had to quickly reshuffle and get organised and I thought we were absolutely outstanding.
"We didn't look like we had 10 men and that's a big credit to the players. Tactically we were brilliant. It was a great performance and I thought we had great control of the game without the ball.
"I think you've seen the steel in my team and the belief, and that's something that we've got. We had to show resilience and I am very proud of my players."
Nottingham Forest boss Billy Davies felt the red card worked in Swansea's favour on the night, although the Scot believes they could pay for their exertions in the second leg.
"Although I think it was a red card, at the time I was disappointed because I knew they would start defending deeper and that wouldn't help us," said Davies.
"Having been a 10-man team and played against 10 men on many occasions, it becomes very difficult and in the first half we were pedestrian and too slow. The second half was much better, we had several chances and we just needed a goal.
"But I said before the game, win lose or draw, it is only half-time, and that is still the case. There is still lots to play for and I am full of optimism for the second game. It is still a very open game that can go either way."
Source: PA
Source: PA