In a hard-fought display the Merseysiders’ victory was sealed by a Stewart Downing strike, with the tie now coming back to Anfield for the second leg.
Rodgers was happy with the display of his side and downplayed injuries picked up by Glen Johnson and Joe Cole.
“It will take time until Liverpool start playing the way Swansea did last season (tactically),” he told Sky Sports after the win.
“Actually the way you play depends on the players you have.
“As for today I saw two things which were very important for me, I saw desire and commitment. I am very grateful to my players for a good game.
“Obviously it was a serious test of the players’ fitness and I am really happy with the result.
“This was my first competitive game in charge of Liverpool and for me it didn’t really matter whether the game was played in Belarus or Brazil as I am really honoured to manage this side.
“The substitution of Glen was planned and as for Joe the injury is not serious and more of a precaution,” the Northern Irish coach confirmed.
By Gareth McKnight