The Foxes briefly extended their lead at the top of the Championship to four points after Harry Winks scored a 94th-minute winner to cancel out substitute Josh Maja's 89th-minute equaliser.
Kiernan Dewsbury-Hall had put Leicester in front after 72 minutes before unselfishly opting to set up Winks at the death.
"It was a very difficult game because of them and because when you play Wednesday night and Saturday lunchtime it's not easy, and they played Tuesday night, so they had 24 hours more to recover the energy," said boss Maresca.
"For me it's unbelievable when you play Wednesday night and Saturday both teams have to play together (at the same time), not one on Tuesday and one on Wednesday because the difference is huge." Maresca claimed some of his players were tired during the game.
"Wilfred (Ndidi) came back from a long-term injury, we gave him some rest on Wednesday, but you could see he wasn't fresh," added the Italian.
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Maresca, who started his professional career at West Brom and played 47 games there between 1998-2000, will have been relieved as there was little between the teams, who both hit the goal frame in the first half.
West Brom had a penalty claim turned down when Grady Diangana went down after it appeared he was pushed over in the box; VAR might have intervened if it was available.
The home side went close in the 25th minute when Cedric Kipre stabbed against a post with the goalkeeper beaten after Matt Phillips's corner had flicked off a couple of heads.
But Leicester returned fire to hit the goal frame themselves when Kelechi Iheanacho's low angled drive was deflected on to the near post by Darnell Furlong's lunge.
After the break, Ndidi got on the end of a cross from sub Abdul Fatawu, but his flicked header under pressure lacked the power to beat Alex Palmer, who fumbled before the ball was cleared.
The Ndidi-Fatawu link-up combined again to devastating effect in the 72nd minute.
Fatawu spotted Ndidi's run in the inside right position and the latter crossed for Dewsbury-Hall to nod the ball home ahead of Furlong from six yards out.
Albion equalised in scrappy fashion. Furlong's throw-in was headed away by Faes and, when the ball came back in, Kipre helped it on a grounded Leicester defender could only tee up Maja to prod home.
But Leicester hit Albion on the counter-attack when they broke on a long throw-in and Iheanacho passed from inside his own half to Dewsbury-Hall, who ran 40 yards before slipping in Winks for an open goal.

Winks leaves it late to stun Baggies

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