Leading scorer Sam Winnall fired the home side in front after 22 minutes with his 18th goal of the season and also hit the crossbar with a second-half header.
But substitute Steven Gillespie rescued a point for hard-working Rovers in the 89th minute.
The 1-1 draw extended the Iron's unbeaten run to 17 matches but they fell two points behind leaders Chesterfield, who won 4-1 at Cheltenham.
"It is always very disappointing to concede a late goal," said Wilcox, whose team was booed by some supporters at the final whistle.
"We were nowhere near our best, I am not going to hide from that, but we have still managed to take a point and stretch our unbeaten run to 17 games.
"We have got to try and manage expectations here. Scunthorpe as a club have just had three terrible seasons, two of which have ended in relegation. But now here we are second in the table and unbeaten in 17 games.
"We need to embrace that and enjoy it. We are now coming towards the part of the season when it can get a bit nervy.
"It's the time when we need everyone pulling together."
Even though not at their best, Wilcox insisted Scunthorpe should still have managed to win the game.
"We have hit the bar, had two or three penalty appeals turned down and have created most of the chances," he said.
"But there were two teams out there and Bristol are a good team. I saw them beat Burton last week and knew what they were capable of."
- Sports & Recreation
- Steven Gillespie