Fans’ frustrations boiled over, with the first audible shouts of ‘We want Lambert out’ from home faithful this season.
The home side struggled to break down the seasiders, bottom of the Bet Championship, and needed Christian Benteke’s 88th-minute winner to squeeze through.
Villa have scored just twice in six games and have won only three of their last 17 outings, but Lambert said he did not understand the chants minutes before the Belgium international’s late strike,
“When you are dominating the game and the lads are patient then it’s a bit strange,” he said. “The goal was a great goal and I knew the way we were playing we’d get something.
“They are entitled to say what they want.
“I’ve had it all my career at times but it doesn’t do the lads any good, it doesn’t do the team any good. The players have been great but don’t get me wrong, they’ll be hurt by it.
“We had a lot of the ball and you just have to keep knocking on the door. You have to keep patient and building up and all credit to the team for doing it. We were not struggling.”
Benteke, who also hit the post, struck his third goal of the season to edge Villa into the fourth round.
Lambert added: “The last few games Christian has had big chances but he has just come back from an injury and I said it would take him six or seven games to get to full speed. It was a great goal.
“We deserved to win the game, it wasn’t a relief. It’s testament to ourselves that teams are filtering right back. It’s never easy to unlock a team.”
Lee Clark, who has won just once in 11 games as Blackpool boss, was pleased with his side as they came close to earning a replay.
Andrea Orlandi and Ishmael Miller forced Shay Given into smart saves and Clark urged his men to take the positives.
He said: “The level of performances, with exception of the Bournemouth game (a 6-1 defeat) have been high. We need to turn them into wins but we are pegging back the teams above us.
“We have a lot of youngsters coming through and a lot of positives to take. We have to make sure, in the second half of the season, we stay in the Championship.
“It’s unfortunate and it doesn’t make you feel great. Our fans would have enjoyed a replay or to get through.
“We have to move on and take it into the second half of the season.”