"We want to be having more of an impact on our own season rather than putting dents in other peoples’"
The Republic of Ireland international admits the Toffees missed a great opportunity to end their woeful Merseyside derby record – now 17 without a win – in the goalless draw at Goodison Park.
Sunday’s result left Liverpool a point behind Premier League leaders Manchester City, while 10th-placed Everton are currently 19 points off the top six.
And Coleman says he is more concerned with improving his own side’s position than Liverpool’s battle at the top.
“I’m more pleased with the performance and more disappointed we haven’t got the win as I thought they were there for us and we didn’t happen to get the job done,” said the defender.
“We can only worry about ourselves and we can only be better but, late on, you could feel they were playing for something massively important and that is all credit to them for the season they are having.
“It is going to be a tough battle between them and Man City but we want to be having more of an impact on our own season rather than putting dents in other peoples’.”
The performance more than the result, plus the midweek victory over Cardiff, has helped ease some of the scrutiny on manager Marco Silva.
Since losing the derby at Anfield on December 2, the Toffees have accrued just 15 points from a possible 45, winning only four of 15 league games.
But Coleman believes the players have to take responsibility for what has happened on the pitch.
“It’s one of the things I don’t like about modern day football; it always seems to go on the manager’s toes and us players seem to get away with murder a little bit,” he added.
“I think there is a lot of emphasis on teams doing badly and people wanting managers to lose their job. It’s something that I don’t agree with.
“I think managers need time and the manager here is working very hard. It’s not going to happen overnight or one season.
“He needs to get his own players in, implement his own style of play. That goes for all around the league. I think owners need to be a bit more patient.”