However, they failed to break down Fulham and had to settle for a point at Filbert Street.
Leicester have failed to win any of their four home games, but Taylor will have been heartened by the rousing reception his team received at the end.
They played some good football and troubled a Fulham side, who are finding the Premiership a much tougher proposition than the First Division.
But Leicester were on the back foot in the second minute when Fulham striker Louis Saha raced to the byline.
Saha cut the ball back into the path of new £11.5million signing Steve Marlet, who was left unmarked but he completely missed his kick.
It was an un-nerving moment for Leicester, who had shipped 14 goals in five league games.
Saha then skipped away from Matt Elliott, only to see his shot go high into the crowd.
Leicester retaliated in the 11th minute when Jordan Stewart got away down the left and sent over a cross but Dean Sturridge's header went over the top.
Fulham had a scare in the 18th minute when Robbie Savage played a quick free-kick down the channel to Scowcroft.
He released Sturridge, but keeper Edwin Van der Sar raced out of his goal to divert the ball to safety.
Fulham were playing some nice football and won a free-kick when Savage bundled over Saha.
Lee Clark floated the ball into the area, but Marlet could not get any power on his header.
Leicester defender Frank Sinclair then picked up the first yellow card of the game for a body check on Rufus Brevett.
A poor header from Stewart gave Fulham an opening, but keeper Ian Walker managed to block Clark's shot from just inside the area.
Leicester manager Taylor was clearly unhappy with Sinclair as he took him off in the 34th minute and brought on Gary Rowett.
A minute before the substitution Taylor's side almost took the lead when 19-year-old left-back Stewart again found space on the flanks.
He picked out Sturridge with a pin-point pass, only for the striker to drag his effort wide.
Leicester seemed to be growing in confidence as half-time approached and Scowcroft tested Van der Sar with a header following a free-kick from Dennis Wise.
Stewart then tried his luck from 30 yards in the 48th minute after latching onto a pass from Izzet.
His shot carried plenty of power but Van der Sar was not troubled as the ball whizzed past the post.
Fulham midfielder John Collins then fed Brevett on the left and he delivered a cross into the box. Marlet peeled away from his marker and tried a spectacular volley that went narrowly over the top.
Fulham should have taken the lead in the 57th minute when Clark picked out Sean Davis in the area.
His first touch was good but from six yards he only succeeded in finding the side netting.
Leicester hit back and Stewart played the ball into the path of Izzet and his clever lob beat Van der Sar but was just wide of the target.
Then Sturridge flicked a header the wrong side of the post after a fine delivery by Lee Marshall.
Leicester stepped up the pace and Stewart, who was having a fine game, swept the ball into the path of Scowcroft but his header went over the crossbar.
Then Stewart limped off in the 79th minute after falling awkwardly and he was replaced by Andy Impey.