"The match came on the back of a very, very demanding game against Aston Villa," Houllier said.
"The long delay not withstanding at Villa Park, we had to really search right to the end to get a good result in that game.
"And I thought we lacked a bit of freshness against Everton because of that. But if we were short of confidence and freshness, we certainly were not short of character.
"To me, that is a good sign for the future.
"We have put an end to the pattern of consecutive defeats in the Premiership now and we kept a clean sheet, which hasn't happened for some time.
"We stood up to the physical challenge from Everton and if you could hear the celebration from their dressing room after the game, you would know they were very happy with a draw.
"At some stage you need to break the pattern of losing games. You can't expect to come back with a 3-0 or 4-0 win after a bad run. It takes time for confidence to come back because four defeats plays on the mind of players.
"To get out of that spell you need to be strong mentally, pull together and keep trust.
"From where we are coming from, it has not been a bad week.
"The glass is either half full or half empty. For this week, things are not too bad."
