Jordan Henderson played in Liverpool's 1-0 FA Cup win over Blackburn last night just hours after his wife gave birth to his second child.
Rodgers reserved special praise for his captain Henderson, who produced the assist for Coutinho's winner, after the midfielder insisted there was no way he was going to miss the quarter-final replay against the Championship side.
Rodgers explained: "His wife had a second child during the night so he had to go away, hadn't slept so much, travelled all the way back again and put in the performance he did tonight. It was a real captain's performance.
"He said to me, 'Boss, as soon as the baby's out, I'll be coming back'."
Rodgers thought the much-publicised review meeting he held with Liverpool's players on Sunday paved the way for them to get back to winning ways in the FA Cup.
The Reds boss had denied a report that an internal meeting following the 4-1 defeat to Arsenal had descended into crisis talks and his players responded on the pitch by booking their spot in the FA Cup semi-finals at Wembley with a hard-fought 1-0 replay victory over Blackburn.
Philippe Coutinho's brilliant finish into the far corner with 20 minutes to spare was the difference between the two sides and Rodgers attributed the improved performance to Sunday's gathering with his squad.
"There was a lot made of that," he said. "I'm a coach who speaks openly to players. Part of the coaching philosophy for me is about reviewing and reflecting performance.
"It's something that we've done all year when we were winning games. That provides us the lever to move forward - how can we be better, how can we improve?
"Because we lost a couple of games, there's a lot been made of that meeting but that review was very, very important in how we want to work. If you don't review and analyse your performance how can you get better?"
The stakes at Ewood Park were high for the Reds, who had fallen behind the Barclays Premier League's top four following successive defeats, but their manager quashed suggestions their entire campaign had hinged on this result.
"I'd seen all of this about saving our season, it wasn't about saving our season," he added.
"We want to compete at the top end of the league and want to win a trophy this year - that's been clear.
"For us, we just needed to stay calm in the game and focus back on our performances. Our two performances against Arsenal and Manchester United weren't to the standards we'd set for three months."
The hosts had chances to cause a cup upset, most notably when Simon Mignolet produced saves in quick succession from Tom Cairney and Ben Marshall early in the second half, and it was the man between the posts at the other end who almost beat him in the dying throes.
However, Simon Eastwood's shot on the turn went straight down the Belgian's throat moments before a spirited Blackburn side were afforded a standing ovation for their efforts.
"I'm hugely proud of the team and the whole football club," said Rovers boss Gary Bowyer.
"The supporters were tremendous tonight as well. There's a hint of disappointment because we've not got through.
"We've certainly pushed them over the two games and had a right good go. Mignolet's pulled out several good stops over the two games. We just haven't quite had enough."
Bowyer admitted he would like to see the side who dumped his men out now go on and lift the trophy for their outgoing captain Steven Gerrard, whose 35th birthday falls on the day of the final.
"I wish Liverpool all the very best," he added.
"It would be fitting if they could win it for Steven Gerrard, it would be a great way for him to finish his Liverpool career.
"He's been one of the best midfielders for a long, long time in this country. Whilst I wasn't wanting it to happen, now we're out of the cup I certainly hope it does."