The Whites boss led his side to just their third win of the season last weekend with a 2-1 victory at Annagh United.
Distillery lie second from bottom and are seven points behind Institute in their bid to secure a play off place - with just 10 matches remaining.
However, Murray, who took over at New Grosvenor in November, says he is not being ‘naive’, but is confident his team can still win their fight to remain in the Championship One division.
“We’re still massive outsiders to reach the play offs,” Murray commented.
“Institute have a couple of games in hand on us. The teams realistically that we’re chasing are Armagh and Ballyclare, who are seven and eight points clear of us, but we have a game in hand over them.
“It’s going to be a huge huge task,” Murray said.
“We have a huge job even to get a play off place. Each game now is a cup final for us. We have to be doing everything we can to make sure the team stays in the chase.
“We knew coming in it was a big task and nothing has changed. We have to win a hell of a lot of games, at least seven or eight, if we are realistically to stay in the division.
“We need to put a run together if we are to make it.
“We’ll see what happens,” Murray stated. “I’m still quite optimistic.
“I’m not being naive, but I’m still confident. I have a genuine belief we can do it,” he said.
“We now have the players in who can perform at that level. We’ve got 14 new players in, we’re still a new team.
“We’ve replaced the old squad so we need to find a happy medium between the development of the squad and winning matches.
“I still believe with a wee bit of luck we will be there or thereabouts.
“It will not be until the last few games that we will start to climb out if it’s going to happen.”
The Whites were delighted to aid their task by taking three points at Annagh United last weekend.
“It was a good win, a well deserved win,” Murray said.
“It’s been coming, We had a decent result at Bangor and we deserved the win over Annagh.
“It was spoilt by two players being sent off and the manager Dean Smith being sent off.
“We were well on top and deserved the win, but it was spoilt a wee bit by officials.
“I’m delighted,” he added. “All the new signings are starting to bed in and we’re playing like a cohesive team.
“Against Loughgall we had a bad result, we played like a team that had never played together, which is essentially what we were, but players are starting to settle in and I’m over the moon.”
The Whites face leaders Ards at New Grosvenor tomorrow (Saturday, kick off 3pm), in what Murray describes as a ‘massive game’.
“Tomorrow’s fixture is a massive game for us, they are all massive games, but Ards are coming off the back of a defeat to Cliftonville in the cup final, so they will be out to prove a point.
“They are sitting top of the table. They are set for a play off place to go into the Premier League and they will be looking for a few more wins.
“They are a team that’s absolutely flying, they are the best team in the league, not just because they are top, but on their current form they are the best in the league.
“They’ve won the last four or five matches quite comfortably so it will be a difficult task.
“It will be difficult for them and us, we are a team fighting for our lives.”