Iron midfielder Matty Sparrow rattled the woodwork shortly afterwards, and Adkins felt Scunthorpe merited all three points.
"We were at home and this was a game we wanted to win against a team who will be one of the main promotion challengers this season," he said. "The fact my players are disappointed not to have got all three points is a good sign.
"It shows we have a dressing room of winners who very much want to be involved in the promotion race in the second half of the season.
"We are not talking about play-offs. We want to be in the top two.
The fact that leaders Nottingham Forest have lost means we have missed the chance to close the gap still further on them and so apply the pressure.
"I thought we played well enough to have got all three points and but for a bit of ill-fortune when Sparrow's shot came back off the woodwork, we might have got them."
Tranmere boss Ronnie Moore also felt his side could have claimed a crucial victory.
"We were very unfortunate to come in at half-time trailing," he insisted.
"Scunthorpe were the home team yet we controlled much of the first half.
"It was disappointing to fall behind so close to the interval but I told my players that this game was still there for the taking.
"Scunthorpe might feel they were unlucky on a couple of occasions, but we have shown we can come from behind and played well enough to have finished with all three points ourselves."