The English giants again found themselves in a relegation battle for the second season running, and this time needed a final day win.
Abdoulaye Doucoure secured it with a wonder strike against Bournemouth, ensuring Dyche's first five months at Goodison Park didn't end in catastrophe.
The former long-time Burnley manager took over the side from Frank Lampard in January, but wasn't able to guide them away from danger, needing the final day to get the job done.
But he explained he was always confident of beating Leeds and Leicester to the remaining spot in the top flight.
"I had total belief when we got there," he said. "We just had too many injuries, the strikers weren't in form, we had no fullbacks, we had to change the shape.
read more everton
EDGE
Tony Bellew calls Cundy a 'weasel' after Everton secure survival on final day
Doucoure stunner keeps Everton up on dramatic final day and fans invade pitch
"On the other hand, because those decisions were made early, we could work on that all week so I went into the game confident we could get something."
Discussing the day on Merseyside, he continued: "I didn't know it was going to be a magical goal like it was that did the job, but it was nervy and it was difficult.
"As I said after there was no glory in that for me, there is when it's done, of course, we're Everton Football Club, but they're ugly games, they're really really tough games, very taxing on players, managers and of course the fanbase, but when you get it right it's a glorious feeling."
When the full-time whistle came, fireworks and celebrations greeted the victory, but Dyche knows his half-season hasn't been good enough.
Most read in Football
Man United FA Cup final blow, Guardiola reveals surprise decision, Mourinho charged
Man United suffer another injury blow with £90m man set to miss FA Cup final
Lingard becomes free agent as Nottingham Forest confirm exit after season to forget
I offered out Ferguson and instantly regretted it when he waited in the tunnel shirtless
"I expect more from the Everton players and myself so I expect us to not be in that position," he explained.
"I thought we did a lot of work to not be in that position, there's been a lot of injuries and suspensions and all that but I was more like 'what are you celebrating really?'
"We're Everton Football Club and I'm Everton manager, I'm not celebrating just scraping by, that's not what I went there to do. Of course it's a longer term job to remodel it and reshape it and move forward again."