Balint Bajner’s dramatic stoppage-time equaliser stretched the Magpies’ unbeaten run to five games and moved them to within goal difference of escaping the League One relegation zone.
And Dutch manager Moniz, overseeing his first home game in charge since succeeding Shaun Derry, admits County must build momentum with just four games left.
“The results mean we are only goal difference from being out of the bottom four and this is very positive. We have to take advantage,” said the former Spurs skills coach.
“It was a fantastic goal from Balint, but I knew after 60 minutes Barnsley would break and I told the guys that. With the way that we were playing, I always thought we had the capacity to score the equaliser.
“I am delighted for the fans because they saw an attractive game. It’s a dream to have this kind of ambience and I want to thank them on behalf of the group.
“They gave us the energy to go on because they were not cynical or negative. They were behind us and we had 12 men. This point is for the crowd.
“But it still feels like a defeat because we always go out with the intention of getting three points.”
Barnsley striker Sam Winnall opened the scoring in the ninth minute when he lashed in a terrific half-volley from the edge of the box.
Gary Jones cracked a shot off the inside of the post for County before Winnall then hit the post for the Tykes.
It was the turn of the crossbar to keep Notts in the game early in the second half when Conor Hourihane saw his effort almost restore the visitors’ lead.
However, Bajner struck a low shot beyond Adam Davies from Will Hayhurst’s cross in added time to salvage a point for the hosts.
Barnsley boss Lee Johnson said: “I thought we should have won the game. We hit the post, we hit the bar and there should have perhaps been a sending-off.
“We’ve had a one-on-one with the goalkeeper which we should have scored. Obviously key things happen in games and that’s where you’ve got to take advantage.
“We didn’t, for whatever reason, but to be fair to Notts County they kept going. They are fighting for their lives and it’s a case of beware the wounded animal.
“They are always going to throw caution to the wind, but we had enough breaks that we should have done better with. We just needed a better final ball that could have set us off.
“The boys worked ever so hard, but in the spell just after half-time, we just didn’t have that calmness.
“That’s the difference between the top sides and sides like us who are hoping to be one.”