Scoring a brace, the 24-year-old scored his first ever league free-kick to beat Petr Cech from 30-yards and make it 1-1 before half-time, later capping off a 19-pass team move with a close-range volley after the break.
Coutinho has been the leading light in Liverpool's last two campaigns, finishing well short of Champions League qualification in both, and it is expected he will continue to be the talisman now he is supported by a stronger attacking line-up.
So much so, Henderson expects the playmaker's performances to put him on a par with some of the best players across Europe.
Captain has huge praise for "fantastic" Coutinho
Speaking to the Liverpool Echo, the Reds captain noted how Lionel Messi, Cristiano Ronaldo and the club's former No.7 Luis Suarez are "seen as the elite players in world football."
He declared: "Philippe has certainly got the talent, the work ethic and the hunger to get into that bracket. He's a fantastic player for us."
Henderson said that he has "seen him develop as a player" in his years at Liverpool and acknowledged that he is "still only 24."
The midfielder insisted that if Coutinho "continues to work as hard as he does" and "continues to develop like he has done" then he is "sure" that he will "be in that bracket before long" because he's still only "very young."
Henderson hoped that it "won't be long" before people regard Coutinho "alongside the Messis of the world" and insisted for Liverpool it is only a matter of trying to "keep him fit" and "keep him playing like that" because of how "brilliant" he was at Arsenal.
Coutinho's Man of the Match performance at the Emirates Stadium was the obvious highlight of a mixed display which showcased Jürgen Klopp's side's attacking potential and their defensive inconsistencies.
Henderson insisted it was "a good win" for the team which they "of course" would "have taken before the game."
Henderson notes need for improvement at the back
But despite being "pleased with the three points", the skipper admitted that there are "things we need to improve on before the weekend" and their trip to newly-promoted Burnley.
The 26-year-old cited that they "didn't play as well" as they might "have liked" in the first-half and said: "We just didn't get going until after they scored."
He suggested that their "last 10 to 15 minutes" of the first 45 "were better" because they "kept the ball better" and "Philippe came up with the goods to get us level."
"It was a big goal - an unbelievable strike," Henderson said of Coutinho's leveller on the cusp of half-time, noting that they "grew into the game" and "looked a lot more confident" after that.
He revealed that Klopp "spoke at half-time about the things we needed to do better" and insisted that they "did that in the second-half."
Midfielder excited by Liverpool's striking options
Henderson took plenty of heart from the way in which Liverpool tore through Arsenal's defence inside the first 18 minutes of the restart, Coutinho, Adam Lallana and Sadio Mane all netting to give the visitors a significant advantage.
The England international says that, while they can defend better, the array of options and qualities Klopp has available in the final third is a tantalising prospect.
He insisted that they have "got a lot of talented players" going forward and "looked very dangerous at times" against Arsenal with their "pace and creativity" in the final third.
Henderson said that they "scored some great goals" but also vowed that they "need to be solid defensively and provide better protection" for the back line.
"When Arsenal scored their second they gained momentum and we sat back a bit too much, inviting pressure," he continued, calling it "something we need to work on."
But he was pleased that they "saw the game out" and "got the three points" which he said was "very pleasing."
Henderson added: "We all know we can do better. Burnley will be a different test and a tough test. We need to keep working and keep building as a team."