Goalscorer admits team could have been "two or three" down before half time
The Toffees found themselves a goal down at half-time courtesy of Raul Meireles' strike, but goals from Distin and then Jermaine Beckford put them 2-1 ahead before a Dirk Kuyt penalty ensured honours were even in the Merseyside Derby.
Distin, who played a key role in Everton's defence throughout the game, was pleased with how his team responded to being behind at half time and speaking to Sky Sports after the game he was pleased with the team's reaction in the second half.
He said: "We could have been two or three goals down, but we showed a good reaction at half time and came back strong and conceded a late penalty but I think overall it was a good game for us.
"We showed good character and I'm quite happy you know. We won at home and drew here so it's ok."
When asked whether he felt Liverpool had been inspired by the reception Kenny Dalglish received from the home fans, Distin admitted that the home team were always likely to respond well with the quality of players they have available to them.
He said: "The players are going to have a reaction at some point, it's a good team and a stronger squad and good individuality as well.
"We knew it was going to be a tough game but I think it was down to us. We didn't play our football in the first half but came back with better intentions in the second half and that made the difference."
Distin's goal came from a corner two minutes into the second half after Liverpool had been forced into a half-time substitution with Daniel Agger replaced by Sotirios Kyrgiakos because of injury, but the defender felt this switch made little impact on his goal.
He said: "At this level things are sorted before you go back onto the pitch. We tried a few different settings for corners and I made one or two mistakes in the first half and I felt like I had to do something to catch up and I did so I'm happy about it."