Pools’ League One opponents played the majority of the game with 10 men following Billy Sass-Davies’ early red card. They then took the lead in the second half through Callum Ainley with what proved to be the winning goal.
Following the result, Challinor said: “We're disappointed because we felt it was an opportunity and after 15-minutes it was an even bigger opportunity which passed us by.
“It's disappointment but that becomes more depending on the draw tomorrow night.
“It was a resilient [performance] from them. It reemphasises where we need to improve, I thought we were a little bit toothless up the top end of the pitch and conceded a poor goal from one of their fleeting attacks. I can be critical but it's pointless reemphasising a point we already knew.”
The Pools boss also admitted Crewe were hard done by the early sending off as he felt Tyler Burey committed a foul before being brought down.
“It didn't make things more difficult them going down to 10-men,” he added. “I'd rather play against 10 men and it put it on us to take advantage but we were just too slow in our passing in the first half.
“Tyler has pulled their lad and he's reacted and pulled Tyler down. Once the referee doesn't give the first foul he has to send the player off.
“The referee missed the foul tonight and we were on the right side of the decision but we couldn't capitalise on that.”