The Reds dominated the opening Premier League game of the season and emerged victorious thanks to Daniel Sturridge's first-half strike, but they squandered a host of chances and needed Mignolet to keep out Jon Walters' penalty to seal all three points.
It was Mignolet's debut for Liverpool following his summer move from Sunderland and Rodgers was delighted with his goalkeeper, but also paid tribute to the rest of his players.
"Obviously when you don't take your chances - and we created numerous chances and didn't do that - and then get a penalty against you at the end, there's sometimes that sinking feeling," Rodgers said at his post-match press conference.
"But he'd done his homework and knows exactly where all the penalty takers are going. It was a good first save and then obviously the reaction to get up and make the second save was impressive.
"I think from that, you also saw the spirit in the team, what we're trying to cultivate here as well and the energy and attitude of the players.
"It was a terrific performance all round - but of course, the goalkeeper gets the plaudits when he saves a penalty right at the end."
Kolo Toure and Iago Aspas were other summer recruits to start the game and Rodgers was pleased with the contributions of the pair, while he also noted an excellent game for Sturridge.
The manager said: "When we lost Jamie Carragher last year, we were losing real experience - but Kolo comes in and offers that. He was excellent.
"Mignolet was very good and Iago Aspas is a real bright and clever player. In and around the edge of the box, he wants to shoot, he wants to combine with people and that's something that's important for us. I thought for 70 minutes he was excellent.
"Tactically he understands the game and what we're trying to do here. All across the board, it was very good."
On Sturridge, who returned from injury ahead of schedule, Rodgers added: "Considering he's only been back just over two weeks from his injury, I think he's a great credit.
"It was a really good move (for the goal), we showed great patience to pass and to probe to get the space. You saw Daniel's power, he's got a wonderful left foot and it was terrific finish."