Jobi McAnuff doubled their advantage and despite Freddy Eastwood reducing the arrears, Rasiak added a third to seal maximum points for the visitors.
"There is always pressure in football and I thought we were excellent," Rodgers said.
"There was a lot of tempo and I talked to the players about controlled passion.
"We had a great start and I have kept enforcing to the players the importance of a strong start. The players had good motivation going into the game and we put quality balls into the box.
"Grzegorz did what he does best and that gave us a good start. It was important we built on that and created other chances and thankfully we took them today.
"McAnuff has been excellent on and off the field since he came in. He's a great motivator for a lot of our players and the supporters love him."
Beleaguered Reading had the ideal start when McAnuff sprinted down the right wing to deliver a cross to the far post where Rasiak headed the ball over keeper Dimi Konstantopoulos into the top corner of the net.
The Sky Blues had a goal disallowed in the 15th minute when Eastwood headed in Michael McIndoe's free-kick but the striker was rightly adjudged to be offside.
The Royals' travelling army of fans were celebrating again in the 54th minute when Martin Cranie attempted to clear a cross but instead gave possession to McAnuff on the right of the box and he drilled a low shot into the far corner of the net.
Coventry's attacks were rewarded when Eastwood grabbed his first goal of the season with a 25-yard shot.
Reading showed excellent composure to continue to attack their hosts and when McAnuff's 20-yard strike crashed against a post, Rasiak reacted immediately to fire home a close-range shot in the 72nd minute.
Coventry manager Chris Coleman said: "Defensively we have conceded silly goals again.
"There are a lot of disappointed young players in our dressing room but they will be better for this experience.
"We had a very, very young team and when you concede a goal like that, your bubble has burst before you have started.
"We made one or two decent chances and we didn't capitalise on that.
"We have to pick ourselves up it is as simple as that. We have a young disappointed dressing room who have never been in this position before and it will be up to the senior players, myself and my staff to pick them up."