Dejan Lovren headed home Adam Lallana's second-half corner to clinch the win.
"We are really pleased and satisfied with the performance of the team," he said. "Especially in the second half we were much superior to them and were able to develop how we wanted to play.
"We fully believed from the start. The secret was not conceding.
"In the second half we came out correcting what we hadn't done in the first half, when we were hanging back too much defensively.
"We were faithful to the philosophy of how we wanted to develop our game and over 90 minutes we were superior to them and were able to capitalise on the chances we created.
"Boruc was outstanding today but the rest of the squad were outstanding. It is not easy to come here and win so to do that makes us really pleased.
"All the players need to be congratulated on a great performance."