After a great 1-0 win at Hartlepool United on the opening day, Kinnear's Whites were full of confidence ahead of hosting a Kent derby with the Ravens - watch match highlights here.
But Joshua Rees gave the visitors a first-half lead and then Louis Dennis added another in the second half although Dover did hit back quickly through David Gregory's own-goal.
It wasn't the start Kinnear wanted at Crabble but took confidence from the amount of chances his side created. He told the club's website: "You've got to get the ball in the net, we did everything but their keeper has pulled off some good saves. It was probably as many chances as we've had in any game over the two and in pre-season.
"We're all disappointed. We got caught twice with sucker punch goals, when we trying to get at them. That's what the lads have got to learn. They're young and this is what's going to happen. People are going to come to Dover and get behind the ball, slow the game down and stop us.
"At least we created a lot of chances and second half, didn't feel sorry for ourselves."