Luis Enrique's Spain had been subject to boos from their fans along with media criticism following 0-0 and 1-1 draws with Sweden and Poland respectively in their opening two Euro 2020 games, both in Seville.
A lot of the attention has centred on forward Alvaro Morata, who missed an early penalty against Slovakia, but Luis Enrique's side turned around those woes with an emphatic display, securing the biggest win of Euro 2020 so far.
The victory also equaled the largest margin of victory in a game at the European Championships, Spain becoming the fifth different side to win by five goals in the tournament (after France and Denmark in 1984, the Netherlands in 2000 and Sweden in 2004).
Aymeric Laporte, Pablo Sarabia and Ferran Torres all netted along with two own goals as Spain secured second spot behind Sweden in Group E, setting up a last-16 date with Croatia.
"I believe people can have plenty of complaints, but I really don't think there can be any criticisms of today," Luis Enrique told his post-game news conference.
"We will prepare for the last-16 with plenty of confidence and we're desperate for Monday to come around soon."
He added: "It is a relief. Not just for me, but in terms of what it means with our ability to achieve a convincing result with our style."
The former Barcelona boss added that they would "pop a bottle of Cava" to celebrate their progress but wanted more in the knockout stage, with his lofty expectations unchanged.
"We will go step by step. I've spoken about what I believe we can achieve and the expectations we have as a national team and I haven't changed my opinion," Luis Enrique said.
"We have certainly popped that bottle of Cava, therefore we are delighted, we are pleased the fans and players have had a good time.
"Now it's time for us to get another bottle of Cava and see if we can pop that too."
Spain will take on Croatia in Copenhagen on Monday, with the teams last meeting twice in 2018 via the Nations League.
Croatia won 3-2 in Zagreb, while Spain thrashed the 2018 World Cup finalists 6-0 in Elche in those encounters.
"They are a top team with players we know well, we played in the Nations League two years ago as well," Luis Enrique said.
"It will be a tough match but when you get to last 16 you can't expect easy teams."