The Glovers twice led at Bloomfield Road only to be pegged back by a Nathan Delfouneso strike deep into nine minutes of additional time after a nasty facial injury to Ryan Dickson.
Francois Zoko and captain Darren Ward had twice but the Green and Whites ahead, with the Seasiders notching two controversial goals through Delfouneso and Kelvin Mellor.
With the Lancashire outfit last conceding two at home in mid-December, Way felt the team deserved more.
“I’m just really pleased with the team’s performance,” he told YTFC’s official YouTube channel.
“You only have to see the subs that Blackpool made – they’re a big club and we’re competing. Everyone is giving everything around the Football Club; all staff, all players.
“If we pick up one or two results at home now we’ll look at the Wycombe game (1-1) and Blackpool and they’ll turn out to be good results.
“I’m proud of the players today, they didn’t deserve to let two bad refereeing decisions cost them three points.”
The Glovers felt referee Carl Boyeson missed a handball in the build-up to Mellor’s equaliser before wrongfully penalising Town in the closing stages with the Seasiders scoring from the resulting set-piece.
Despite those decisions testing Way’s resolve, the Glovers manager was buoyed by the squad’s tenacity and determination.
“Everyone is playing their part at the Football Club,” he said. “That’s what gets me excited and makes me sleep straight at night, everyone giving everything.
“We’re building every day and every week considering we don’t have huge resources.”
The Glovers head to Luton Town on Tuesday in the Checkatrade Trophy, with ticket details available here.