The Easter Road outfit still face a fight to force their way back into the top six in the Premiership with only seven matches remaining before the split.
But the goals from Flo Kamberi and Marc McNulty against Accies allied to St Johnstone’s draw away to Rangers means Milligan and his team-mates are now only three points off that initial target.
The veteran Australian said: “The table doesn’t lie. We are where we are because that’s where we deserve to be at the moment.
“But I don’t think it’s too late to turn that around – and that’s what we’re focusing on. We have to keep moving forward.
“It did hurt us as players, knowing we were in that position. And you could look around the dressing room knowing that, individually and as a unit, we had more to give. Now’s our shot. We’ve started well – and need to carry it on.”
Hibs face Dundee at Dens Park on Friday night before travelling to take on St Johnstone in Perth five days later in what looks like being a crucial match if the Capital side are to reach their objective.
Milligan said: “We can only aim for the teams above us. To do that, we need to win the games in front of us and keep improving – we need to be better than we were overall on Saturday.
“In patches, we were good but we need to work on our game management and try to get into the top six. We know we have the players to do that.
“We definitely have the player to turn this season around. We are fortunate that it’s not too late. We can only focus on what is right in front of us, which is this week’s training, and I’m sure we’ll get more information. But we have good players who are willing to learn and we can grow as a team.
“We went through what we went through. That’s always there. But we can use that to spur things on. We know we are a better team than the points we have put on the board so far.”
Milligan believes the arrival of Yorkshireman Heckingbottom and his assistant Robbie Stockdale can bring the stability required following the period of uncertainty caused by the departure of former head coach Neil Lennon.
He said: “It’s always difficult when there is a bit of unrest, but now that we have a new manager in we can just focus on what he wants from us. That’s the best way.
“We can take away all the other information that is coming in from everywhere else and single in on what he wants. When you win it’s much easier to improve the mentality and keep the performances getting better.”