Coutinho scored the only goal of Wednesday's FA Cup quarter-final replay win over Blackburn at Ewood Park on Wednesday, burying a low finish across goal after he had played a neat one-two with Henderson in the right channel.
The victory earned Liverpool a semi-final meeting with Aston Villa at Wembley and kept manager Brendan Rodgers' bid for a first trophy with the Anfield club on course.
Henderson told BT Sport: "Philippe has got a great football brain and the easy bit is just giving him it.
"That little bit of brilliance from him wins us the game.
"We go to Wembley against Villa. I am sure it will be a tough game because they are a good side."
Henderson admitted Liverpool's recent defeats to Manchester United and Arsenal in the Premier League had placed more importance on the FA Cup, with hopes of qualifying for the UEFA Champions League fading.
"It was a really important game for us today," he added. "Everybody has been disappointed the last couple of weeks. We knew it would be difficult for us."
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