Ivan Rakitic's superb volley and a masterclass from Lionel Messi, who hit a second-half brace in Wednesday's 4-2 win at Wembley, will grab the headlines.
But Valverde was quick to highlight the impact of Arthur, who joined from Gremio for the 2018-19 season and has been compared to Barca icons Xavi and Andres Iniesta.
"Man, that's what it's all about," Valverde told beIN SPORTS of the 22-year-old's performance after a win that left Barca level on points with Inter at the top of Group B.
"Looking for a gap, he has some qualities that come in handy. He completes many passes, it's hard to take the ball off him. He has been a starter in an important game.
"We played a good game and we had opportunities to extend the lead before and not have to suffer so much, but this is the Champions League."
Although Arthur impressed his coach, the former Gremio midfielder highlighted Messi's impact and echoed Philippe Coutinho's assessment that the Argentina attacker is the greatest player ever.
"It's amazing what he does, he makes extraordinary things routine," Arthur said to beIN SPORTS.
"He's the best player in history, I'm very happy to play alongside him and learn.
"It was a difficult match, it's not easy to play against Tottenham."
Messi took his tally to five goals from two games in this season's Champions League, as well as playing the pass that led to Coutinho's early opener, while he hit the post twice.
The Barca captain was benched by Valverde for his team's draw with Athletic Bilbao in LaLiga last time out but was in mesmeric form against Tottenham.
"He comes from a hat-trick against PSV," Valverde added. "He has scored two goals.
"He is happy and that happiness is very good for us."