Neil Critchley’s side, who take on runaway leaders Fulham at Craven Cottage on Saturday, are eight points adrift of the top six with a game in hand.
When asked about a play-off challenge, striker Lavery said: “That’s got to be the ambition. We’ve got to be looking up.
“During the first half of the season we’ve more than matched the teams we’ve been playing, so why not? We’ll certainly give it a go.”
The Seasiders next face a rampant Fulham side that have scored 22 times in their last four games and 73 all season. Marco Silva’s men are five points clear of second-placed Blackburn Rovers.
“They’ve been doing all right, haven’t they?” Lavery joked. “So we know we’re in for another top game but every game is tough in this league.
“We know we can match them because we’ve already beaten them this season, which was a win that really kick-started our season. It’s going to be tough but we know what we’re in for.”
Lavery seems to be Critchley’s preferred man to partner Gary Madine in attack at the moment, keeping Jerry Yates on the bench.
The Northern Irishman is enjoying playing alongside the more experienced Madine, who provides the perfect foil for a nippy goal-getter.
“He’s great to play with,” the 23-year-old said. “He drives quite a few defenders away from me, which gives me a lot of space to run in behind.
“If the ball is coming up, it drives a few of the defenders and the midfielders towards him, so he’s great to play with. Hopefully it continues.”
Further competition in the forward department has arrived this month in the form of Jake Beesley, signed from Rochdale.
Lavery welcomes the competition and believes it will only drive him on to perform even better.
“That’s only going to be good for Blackpool, it’s healthy competitition,” he said.
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