The Toffees currently sit seventh in the table, two points ahead of Kenny Dalglish's side.
The Dutchman was involved in Everton's late comeback against Manchester United – a game which ended 4-4 – and has called on the players to take as many points as possible in their remaining four matches.
"These games are the reason I came to play here in the best league in the world," he said. "The season is not over, there are four games to play and we want to surprise some teams and finish high up the league.
"There are 12 points to play for and we want as many as we can get."
Heitinga has been one of Everton's outstanding performers this season, establishing himself at the heart of the Toffees' defence.
The Dutch defender, who is in the running for Everton's Player of the Year award as voted for by the fans, is enjoying what he has called, the best season of his Everton career.
However, the 28 year-old insisted that while this may be his best ever season, there is still much more to come in the future.
"I think this is my best season for Everton so far and I hope I can keep this level up," continued Heitinga.
"It is one of my better seasons – maybe my best as a professional – but I'm only 28 and there are many years to come. I am only looking forward.
"We can't play football without the fans and I am happy to hear some of them are voting for me as that is a big trophy."
Fulham, Stoke, Wolves and Newcastle make up Everton's final fixtures as they look to finish above Liverpool in the league for the first time since 2004-05.