The Cod Army led 3-0 in the first half through goals from Anthony Pilkington, Harrison Biggins and Paddy Lane.
Substitute Aiden O’Brien’s dramatic 95th-minute equaliser ended the visitors’ hopes of a first league win in seven games.
Ronan Curtis pulled one back from the penalty spot in first-half stoppage time before Marcus Harness gave Pompey a glimmer of hope with their second 10 minutes from time.
Crainey believes the penalty which handed Danny Cowley’s side a lifeline was “soft”.
“I’m disappointed,” Town’s head coach said. “The penalty was the turning point in the game.
“I’ve looked at it back and it looks soft. Sometimes you get them and sometimes you don’t.
“Unfortunately the decisions didn’t go our way today, which is a little bit frustrating.
“We have to dust ourselves down. It’s a point on the board and we go again at Wigan on Tuesday.”
Crainey praised his side’s first-half performance but stressed they have to see games out when they dominate.
Town missed the chance of opening up a healthy four-point cushion over the relegation zone.
“I’m really pleased with the group but we have to see that through,” added the Scot.
“We were 3-0 up and then end up drawing the game away. It feels like a defeat but I’m hoping come the end of the season this ends up being a massive point for us.
“It’s a tough place to come Fratton Park. Portsmouth are a good side and there’s some great home backing behind them as well.
“I thought we were absolutely outstanding in the first half of the game and played some excellent football.
“We scored three great goals and then there was a bit of a turning point just before half-time, when they got the penalty and scored that. It changed the context of the game for me.
“The team was excellent in the first half. We were a real threat going forward and we got the three goals. It was really justified.
“The turning point was Portsmouth getting that penalty because I genuinely didn’t think it was a penalty.
“It gave them a little bit of momentum going into the second half and they were shooting towards the home fans in the second half as well.
“It gave them a bit of a life. It’s something we can learn from coming to a place like this and we can take it into Wigan as well.
“It didn’t go our way. It’s frustrating but we’ll go again on Tuesday. We’ll rest up and get a game plan for Wigan.”
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