The two coaches embraced at full time after the Reds’ 4-0 win over Bayer Leverkusen in the Champions League.
While the German champions did maintain parity for an hour, they were eventually battered.
"It can happen that you come to Anfield and lose," Alonso told reporters post-game.
"To lose 4-0 is not nice. They are a top, top team and they punished us. It was a pity we couldn't hold 1-0 for 15 to 20 minutes. They did it against Brighton, they did it against us.
"We were ready to come here and give our best. We did okay for some part but the game changed in 20 minutes. Liverpool are strong. We lacked some power and consistency. Defeat, accept it, congratulate Liverpool and move on.
"I will try to separate the game and the pain from the result to the feelings of coming back and having love. I'm really thankful to have that reception.
"It's early to tell but I can see that Liverpool have a very good balance, a very complete team. They work the 11 players and they have the power to hold a clean sheet which is important in the Champions League. In the Premier League, let's see. It's early to tell but it's looking good."