The Shrimps had looked set for a third straight home defeat in all competitions as they trailed with 10 minutes remaining.
They also played for an hour with 10 men following Shane McLoughlin’s straight red card in the first half for a challenge on Ethan Hamilton.
However, Cole Stockton’s second of the afternoon meant honours ended even ahead of Tuesday’s home game with Lincoln City.
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Robinson said: “I think we’ve cost ourselves with the first two goals.
“We made a mistake for the first one and we gave the ref an opportunity to give a penalty for the second.
“It’s hard to criticise because we showed character again. We made positive changes and went 4-3-2 and, at the end, 4-2-3, but the players make it brave with their mentality.
“We believed we would get one more chance and Cole took it in efficient fashion.”
Stockton had fired Morecambe in front on 15 minutes, triggering a 13-minute spell which saw four goals scored.
Stanley levelled from the spot through Bishop after Liam Gibson was adjudged to have fouled Lewis Mansell.
Mathew Butcher then put Stanley ahead, only for Adam Phillips to level with a near post volley from Arthur Gnahoua’s cross.
Morecambe then went down to 10 men before the break, after which Bishop’s second goal put Stanley ahead before Stockton ensured the spoils were shared.
“Some of the decisions that have gone against us have to even themselves up,” Robinson said.
“The ref believes it was a red card. I’ll have to watch it and, if it is, then it is, but we have to concentrate on what we’ve done after that.”
As well as McLoughlin’s red card, Robinson is also having to deal with another injury issue.
Defender Greg Leigh missed out and will be absent for a few weeks, though it opens the door for Gibson to stake his claim.
Robinson said: “Greg Leigh has torn his hamstring, not the one he originally tore at Aberdeen.
“He will be out for a minimum of four or five weeks. Gibbo (Liam Gibson) had an unfortunate first 10 minutes but he grew into the game.
“He always stands up to be counted and got better and better.”
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