Jadel Katongo was given his marching orders in the 40th minute after hauling down Romaine Mundle when through on goal, the referee adjudging him to have denied a goal-scoring opportunity as the last man.
Despite this, City continued to threaten the Spurs back-line, with Carlos Borges inches away from turning home Dire Mebude’s cross and firing over late-on as the game finished goalless at the Academy Stadium.
And Barry-Murphy praised how his players bounced back from the first-half setback.
He said: “You plan for so much in football but it’s nice to have something you don’t expect and to challenge you.
“Our lads were so good and so brave in the way that they played the game and some of the stuff we did in the second half was very good to see.
“We looked as much of an attacking threat as the opposition who had an extra man so that was really exciting for me.”
The draw continues the Blues’ unbeaten start to the Premier League 2 season with two wins and one draw from the opening three matches.
And with plenty of new faces featuring this season, the EDS head coach was happy with how his new crop are finding the step-up in level.
“It is easy to forget that before the season there would’ve been a lot of question marks over how they are going to adapt,” he said.
“But because the early stages of the season have gone so well we almost think it is normal.
“They have put a lot of effort and hard work into making that transition look so smooth and today it was very good for me to see how they adapted to the difficult situation they faced.”
