Suarez was in the Liverpool starting line-up after completing his 10-game ban for biting Branislav Ivanovic last season, with manager Rodgers recalling the Uruguay forward at the first available opportunity.
He almost scored the equaliser after Javier Hernandez's opener but his second-half free-kick hit the crossbar.
Rodgers told Sky Sports 1: "I thought he was excellent. You could tell he had been out for so long - he probably tired a wee bit towards the end.
"But he's always a threat, I think you could see that, how he rolled out of some actions was fantastic, he went close with the free-kicks, he said he practises them so he's always going to go close with them.
"But I thought he'd done very well considering the length of time he's been out."
Rodgers added: "It only natural (to be rusty). I think sometimes you get games where you come back and that adrenalin gets you over the line in the first game and then probably for maybe a few games after that you start to feel it a wee bit.
"But he's a fighter, his determination is so high he'll recover now and then get ready for the weekend."
While he was full of praise for Suarez, Rodgers appeared to point the finger at Jose Enrique for losing Hernandez at a corner for the goal.
"It is disappointing. It is an individual thing, it is not a collective," he said.
"If you look at the corner you see all the players skin-tight to their markers, no one was free and then Chicarito gets free far too easily.
"It is not good and at the weekend (in the 1-0 defeat to Southampton) we did a similar thing.
"As an individual you have to be stronger mentally and have a greater desire not to lose your marker. If you do that there is a greater chance you won't concede.
"It is not something we go into straight after the game but it is something they know."
As for Suarez, he has pledged to do his best to help the club which less than two months ago he appeared determined to leave.
Speaking after his return to action, Suarez told liverpoolfc.com: "The result is not good because we lost but the feeling is good because we played very well, we created chances and we missed.
"I know it was a difficult moment but for myself and for the team it's very important I'm back because I can help the team and [being] off the pitch I can't.
"We'll keep going for the week and for the next game.
"All the time I try my best on the pitch. I'm here to help the team and help Liverpool and I'll try my best."