The Reds fell behind when Yohan Cabaye's superb volley flew past Brad Jones, however the Uruguayan hit back with a breathtaking piece of skill of his own, bringing down Jose Enrique's long ball before rounding Tim Krul to finish.
The former Swansea boss labelled his star man as a "world class striker", comparing his role at the club to that of Lionel Messi's at Barcelona, while also applauding his teamwork and determination.
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"That was brilliant," the 39-year-old told Sky Sports. "He's been fantastic.
"His first touch coming from that height, and to get that depth on his touch, because normally those touches will go in front of you and then runs to the keeper or to the side. And then [to go] around the keeper was incredible skill and that's why he's a world class striker.
"He plays for us that first number nine role like what Messi does for Barcelona, where he moves freely and others have got to get in behind him to penetrate.
"I think everyone in the game knows he's quality, he's an absolutely fantastic guy and his work rate and intensity is incredible. A great goal for him and he'll be disappointed not to get one or two others."
As for their general performance, the Northern Irishman was delighted with his players' efforts, suggesting they deserved victory.
"I thought we were outstanding," he continued. "I thought our intensity was relentless in the game. We went to sleep obviously just before half time, but for every other moment I thought we were brilliant and deserved the three points, but just couldn't quite put our opportunities away."
Despite dominating proceedings in the first half, Cabaye's strike put the Merseyside outfit behind at the break, however they came out with the same fight and control in the second half, showing no signs of being disheartened.
Rodgers revealed that he just reminded his team to keep their cool, while insisting he is confident they will start recording victories in the near future.
"I just said to stay calm," he added. "Sometimes when you dominate them game like we did and then you concede just before half time it's very easy to come out in the second half and play that desperation football and chase the ball.
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Magpies boss Alan Pardew, on the other hand, was disappointed in the way in which his team conceded, while he was also unhappy that he lost a number of players, with Demba Ba and James Perch limping off.
He said: "No, I felt at 1-0, we lacked concentration for their goal because I thought we were looking comfortable and I fancied that we might have got a second on the break as they were getting more desperate, but the goal changed proceedings a little bit and then of course the sending off.
"It's been a bad day for us, we've lost three players to injury and we've lost our captain [Coloccini] for potentially three games. Not a good day for us."
Fabricio Coloccini was dismissed for a late challenge on Suarez, colliding with the forward well after the ball was gone.
Pardew was unconvinced by the decision to send the defender off though, suggesting the officials got "caught up in the emotion", but was hesitant to critique them due to the "constant criticism" they receive.
"I've seen it a couple of times on the video and it doesn't look too clever if I'm honest," he admitted. "But I genuinely feel that he's kind of trying to stop himself to some extent and he'll be surprised when he looks at it again just as I was.
"I thought [the referee] just got caught up in the emotion of it all a bit, there were a few decisions that I thought were ours and I wasn't sure about the sending off so I just wanted to ask him before he had the chance to look at it again on the TV what he thought of it.
"He said to me that it was serious foul play, but I don't want to criticise referees and I think the morale of referees must be really low. The constant criticism and the issues around them is unfair so I accept his decision, we accept it and other than that I thought he had a good performance."