The Scotsman's goal was his first for the club, capping off a strong performance by the Hammers with the other two goals scored by Michail Antonio and Marko Arnautovic.
Speaking to the club's official website after the game, the 30-year-old winger stated the performance was the result of the effort he and his teammates have put in over the past four weeks.
He said: "I’m really enjoying it. If you see the likes of the forward-thinking players we’ve got with Arnautovic, Antonio, [Felipe] Anderson and [Andriy] Yarmolenko, you’ve got loads of options and people moving off the ball, so when you get that chance, why not try and take it?
“One thing you’ve seen is the fitness level tonight. The lads were great and Aston Villa started a week before us as well, so we’re in good shape and we’re ticking along nicely.
“Anybody watching that first half, and the second half in spells, would see us coming in off the line and the full backs getting around. That’s exactly what the boss has brought to the table.
“It’s good as the boss has come in and his record speaks for itself. He’s phenomenal. The lads have taken to him and his staff straight away and there’s a good feel about the place. We’re working day and night and doing a lot of things to start the season well and get a good start.”
The 30-year-old had a successful loan spell at Villa last season where his displays earned him hero status on the Holte End as he helped them to the Play-off final. Snodgrass made 39 appearances for Villa, scoring seven goals.
At the end of the game the Scotland international applauded the Villa fans at the final whistle, but insisted his future in a different shade of Claret and Blue.
He added: “Listen, it’s great first and foremost to come back and see them, but I’m a West Ham player. I’ve loved my time here when I’ve been involved and playing, but obviously last year I went out and played games and bonded with the Aston Villa fans, staff and players and everyone around the city, so I appreciate them for that.
“But for me, I want to try and get minutes and play in my position. I played tonight and got a chance and it’s great to get a goal, but the performance in the first half was pleasing.
“In my first season and against Wycombe, I was having shots cleared off the line and things, but I took my chance when it came and hopefully it’s the first of many.”
Snodgrass has struggled to nail down a first team spot at the Hammers since his arrival from Hull City for £10.2m in January 2017, and if he is able to impress new boss Manuel Pellegrini, Snodgrass could secure a regular first team place.