The Toffees went into the clash in better form than their rivals but fell 2-0 behind before battling back to salvage a 2-2 draw.
While Liverpool were left to bemoan the referee's decision to disallow a goal that would have given them a late victory, Distin says there were also some mixed feelings in the Everton dressing room.
"We look back with a bit of frustration but I guess we'll be happy after coming back from 2-0 down," the defender told Everton TV.
"It's a draw and we're disappointed, but that shows the ambition and determination of the lads. We once again wanted to win, so right now we feel disappointed. But when you look at the bigger picture, we've lost only one game out of nine in the league."
Distin believes Everton played well enough to take the lead before the interval after battling back to draw level, while they were then frustrated further in a goalless second half.
"They scored two and you just know if they get a third it's going to be nearly impossible to come back, but if you score next, you're back in the game. That's what we did," said Distin.
"I believe we could have scored a third just before half-time and we didn't, but then I thought it would come in the second half. It never came and I think that's why we were disappointed in the end."