The Reds overcame FC Gomel of Belarus 1-0 on Thursday night in a Europa League qualifier and Rodgers was delighted with their players as they balanced a competitive fixture with pre-season preparations.
"I'm pleased and it was an excellent test for us," the 39-year-old told reporters. "Gomel are well into their season so for us it was a great game for our fitness, but it was also competitive.
"It was really special for me as it was the first competitive game. It wouldn't have mattered where the game was, whether it was in Belarus or Brazil, it's an honour for me to manage the club and I'm very proud to lead the players and be their manager.
"Hopefully this can be the start of many more wins and positive games for us."
The Reds did not have the game all their own way and were pushed back by Gomel several times in the match before Stewart Downing popped up to score a long-range effort, just his third for the club since signing last summer.
Rodgers added: "It was difficult and Gomel's tactical idea for the game was to sit back, close the spaces and play on the counter attack. You have to be patient. My message to the players at half-time was continue to be patient and the spaces will start to open up as Gomel tire."I was delighted for Stewart Downing. It was a wonderful strike and that's why we put him on that side so he could come in and shoot."
Joe Cole was substituted during the first half of the match and Glen Johnson departed at the interval, but Rodgers was not worried by the changes, revealing Johnson had been due to only play 45 minutes.
"Glen was only scheduled to play 45 minutes anyway so he was taken off as planned," added the manager.
"Joe just felt his hamstring a little bit. I don't think it is totally pulled and it was just a little bit of tightness so we had to take him off. It disrupted our plans a little bit but it was better to have him come off rather than risk injury."
The former Swansea manager has spoken at length about implementing his passing philosophy at Anfield, after finding great success with similar methods at the Liberty Stadium, and admitted that the squad were still getting to grips with how he wants them to play.
Rodgers said: "How you play the game is based on the players you have. At this moment in time our squad isn't complete and we still have work to do.
"It won't happen overnight and it's going to take time. What I was really pleased with tonight, which is a vital ingredient for success, is desire and commitment. For a lot of the players it was their first 90 minutes so when you have that you have something to build from.
"We have a lot of improvement to make but I am excited in the future we will make those improvements."
Reds striker Luis Suarez, who has been representing Uruguay at the Olympic games, tweeted his well wishes to his club mates.
Suarez said: "I want to congratulate all my colleagues of Liverpool for the win today, congratulations!!"
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