Luis Suarez and the outstanding Jordan Henderson put Liverpool 2-0 up with the Reds bouncing back spectacularly from their FA Cup disaster against Oldham last week.
Arsenal hit back to grab a 2-2 draw in a thrilling game, but Rodgers insisted he and his squad would be in upbeat mood on the journey back to Merseyside.
"It was a wonderful game," Rodgers said. "Normally you would be bitterly disappointed not to have won but I can only be proud of the players, I thought they were absolutely magnificent.
"We never kept the lead long enough and once they get the goal that gives them the momentum.
"We could have very easily won the game but I thought the players were outstanding and really looked a threat tonight.
"I thought Jordan Henderson was brilliant, he scored a magnificent goal tonight that was about his sheer desire.
"He will be a terrific player for Liverpool, he is learning the game tactically all the time and the last few months he has been brilliant.
"We were bitterly disappointed at the weekend but I knew I would get the reaction tonight."