Shrewsbury thank Holt for late point
Shrewsbury grabbed a draw in the 90th minute thanks to the second of Grant Holt's double against Gillingham.
The point means the Shrews are in seventh place in League Two, occupying the last play-off spot.
Simpson told BBC Radio Shropshire, "I was proud of how they responded to a real kick in the guts with the first and second goal.
"If we show that sort of character, we won't go far wrong."
"I hope we're still involved come 2 May," he said. "I hope we do enough to get there.
"We've got another long week to prepare for another tough game at home to Morecambe."
The double took Holt's tally up to 18 for the season as he leads the league's scorers and Gills boss Mark Stimson was an admirer of the striker's display.
"He's the best striker in the league," said Stimson. "When that ball is in wide areas you have to pick him up because otherwise he will punish you and he did that at the end."