Constantine has agreed a deal with Barnsley, with Foyle likely to get Tykes striker Marc Richards as part of that deal. Luke Rodgers is also expected to sign for the Valiants from neighbouring Crewe Alexandra.
Vale's weakness upfront was punished by the Seasiders when the game sprang into life in the second half.
Andy Morrell opened the scoring on 71 minutes when he found space in the box and smashed a low drive past keeper Joe Anyon.
It was a miserable homecoming for Anyon who grew up in Blackpool as a Seasiders fan and his afternoon got worse just four minutes later.
David Fox hit a low drive across the area which took a massive deflection off Vale centre-half Michael Walsh and the teenage keeper was wrong-footed as the ball bounced into his net.
Akpo Sodje claimed a late consolation from the penalty spot but Vale manager Foyle was left scratching his head.
"I just can't understand what more the lads can do," he said.
"The lads have given their all and have kept going right to the end again we've come away without a win.
"Not enough balls went into dangerous areas, but I felt we deserved something for the effort we put in. Getting one back at the end means nothing when we have already conceded two."
Pool boss Simon Grayson added: "I was delighted with the win. I told the lads at half-time that they just needed to be patient and that chances would come.
"We always create chances and I have the luxury of having four good strikers who are all bang on form, it was just a matter of taking the chances when they came along."
Blackpool midfielder Fox insisted the home side's second goal should be credited to him. "It was definitely mine," he said.
"I cut inside the defender and saw the space and hit it towards goal, okay so it took a big deflection and maybe it wasn't going in until then, but I need a goal so I'm claiming that one.
"More than my goal though it was important for us to get another win and it keeps us in the top six and means our challenge for promotion is still alive."
And Pool's other scorer, Morrell, added: "It was not an easy game and we had to work very hard against a decent team who had changed their system, and against the awful conditions.
"But I think we did enough to deserve the win and hopefully now we can stay in the top six at least and really start to push on."
Blackpool moved up to sixth place in the table on the back of this victory, their sixth in seven league and cup outings.
However, next up is a tough trip to improving Leyton Orient, who are fighting for their survival at the wrong end of the table.
Defeat for Vale leaves them eight points adrift of the Seasiders in the final play-off spot, as a season that started so brightly threatens to tail off, especially given the impending exit of leading scorer Constantine.