Joe Allen called on his Wales colleagues to avoid complacency after Hal Robson-Kanu's late goal sealed a 2-1 victory against Slovakia in Bordeaux on Saturday.
Wales' first major international tournament game in 58 years got off to a flying start when Gareth Bale whipped in a glorious free-kick after just nine minutes.
Substitute Ondrej Duda levelled within a minute of coming off the bench but another substitute, Robson-Kanu, had the decisive say with a scuffed winning goal.
But Allen insisted Wales must keep their feet on the ground ahead of their next game at Euro 2016, against England in Lens on Thursday.
"The message was that if we'd lost we wouldn't have been out of the tournament, but that if we win we're not through," Allen told BBC Sport.
"This is one of the games ticked off and three points, which is our best case scenario and I think our focus is now to make sure that complacency doesn't set in in our preparations for the next game."
After being named man of the match, Allen added that Wales did superbly to claim all three points after Slovakia enjoyed their best spell of the game following their equaliser on the hour-mark.
"Never mind my performance, the team was brilliant, great grit," the midfielder said.
"To get pegged back, and for a spell we were against the ropes, but we dug deep like we always do and it's all about digging and grinding. When we got that second goal we were confident we could hang on to it.
"We wanted the same approach as we've had in the qualifying campaign. We've got to work hard off the ball and everyone's got to put a shift in.
"We're a massive threat on the counter with the likes of [Gareth] Bale and [Aaron] Ramsey, Jonny Williams and Hal when he came on, so we know that we can hurt teams.
"This is the type of performance that our fans have come to expect from us and we've got to make sure that we go into the next two games with the same mindset."