The Brazilian playmaker signed from Inter Milan in January for a reported fee of around £8.5m, and Henderson has praised the 20-year-old for the way he has adapted to life at Anfield.
"Philippe is brilliant and I think everyone can see that," Henderson told the club's official website.
"He's a real talent and he's young as well. He has been outstanding since he came into the team and hopefully he can keep that going."
Coutinho claimed an assist for Henderson's equalising goal in the 2-1 win over Aston Villa yesterday, and the former Sunderland man thanked his teammate for the through-ball.
"It was all about the ball from Philippe which was outstanding and I thank him for that one," he said.
"It was a great start to the second half for us and it was a great ball, and thankfully I managed to slot it in, so I'm over the moon."
Liverpool are currently seventh in the Premier League.