Bassett's career at Leicester now embraces six games in charge and only two goals.
Everton had a reasonable excuse for their lack of scoring punch with the absence of Kevin Campbell and Duncan Ferguson.
Leicester had their usual excuse - Ade Akinbiyi's lack of confidence and the continuing struggle of summer signing Jamie Scowcroft to make any great impact for his new club.
Bassett will complete the signing of Brian Deane from Middlesbrough today and hopes the 'special' relation-ship they forged in their years together at Sheffield United can be rekindled.
Bassett said: 'I'm not expecting Brian to turn things around on his own, but he is capable of scoring and putting pressure on my other strikers to get their acts together.'
Everton's future looks bleak on this evidence. Not even the 60th-minute introduction of the new, slimline, Paul Gascoigne made any significant improvement.
Smith consoled himself with the fact that although his side could not score, at least they did not look like losing. The only losers were the paying customers.