Cardiff remain in the bottom half of the table after the draw and, after 11 games played this season, are on 11 points – the same tally at this stage of the campaign the last time they were are at this level.
That 2024-25 season ended in relegation, but the Bluebirds suggested at Middlesbrough there is more to come from this team.
And having had to see the game out with 10 men following a late red for defender Gabriel Osho, Barry-Murphy said they were able to show they have a steelier side to them to go with their ball-retention.
“We had a huge respect for the opponents but we didn’t want to show one sign of stepping back,” said the former Manchester City academy coach.
“We didn’t in the first half, but we still weren’t at our best and I felt as if we could be much better in the moments where we had control of the game.
“In the second half I anticipated us being able to build on that, but it wasn’t possible and we had to show other qualities which are as important as we move through the season.
“We had to accept it wasn’t going to be a perfect game for us in the end. In the end we have to be honest and accept the draw as a good result to back up what was a brilliant performance and result on Tuesday.”