Jude Bellingham's overhead kick five minutes into stoppage time prevented Gareth Southgate's much-hyped side from an embarrassing early exit in the last 16.
Toney, in his first appearance at the tournament as a late substitute, then teed up Harry Kane to head in the winner in extra-time to set up a meeting with Switzerland in the last eight on Saturday.
"I think that was kind of like eye opening, you could be going home any minute," Toney said a press conference on Wednesday.
"The relief after in the dressing room was kind of like 'right now boys, it's time to kick on'.
"I think we've got the character and the quality of players in the dressing room to do so."
Bellingham hit out at England's critics after the game, saying he had to put up with "rubbish" in the media after struggling in the previous two games against Denmark and Serbia.
Southgate also bemoaned an "usual atmosphere" after beer cups were thrown at him in the aftermath of a 0-0 draw against Slovenia, which secured top spot in Group C and progression to the knockout stages.
England arrived in Germany as one of the favourites for the competition thanks to a richly-talented squad that includes the Bundesliga's top goalscorer in Kane, Real Madrid star Bellingham and Phil Foden, who won accolades as the Premier League's player of the year last season.
However, they are just one of a number of fancied sides, also including France and Portugal, who have advanced to the last eight despite underwhelming performances.
"There is always going to be an expectation and there's a lot of people that will always have their opinion," Toney said.
"If we win 2-0, people say we should have won 3-0, 4-0, but that's always the case. We're two games away from a major final and we've just got to do what we can to do it and hopefully it'll be enough."
Southgate admitted after the Slovakia game that Toney had been annoyed at him for being introduced deep into stoppage time.
The Brentford striker said he had to "control his emotions" to reset and play a major role in extra-time in both getting England in front and then seeing the game out.
"By winning," said Toney on how he and Southgate reconciled. "Every player is going to have the hump not playing games, especially when there is one minute to go.
"I had to get out my mood and get on with the game."
All of Southgate's 26-man squad trained on Wednesday with left-back Luke Shaw hoping to be fit to feature for the first time since February against the Swiss in Duesseldorf.
