On-loan Charlton striker Ade Azeez suffered a hamstring injury while playing for Wycombe on Tuesday night.
The Chairboys, who signed Azeez last month on a deal until January 1, 2013, are still waiting to discover the extent of the injury.
The 18-year-old was forced off after just 25 minutes of the Johnstone's Paint Trophy defeat at Yeovil.
It was Azeez's first start for Wycombe following two previous appearances as a substitute for the npower League Two club.
Smith, who was 75, had an association with United which lasted over 40 years.
He signed in 1959 and spent his entire playing career at Tannadice, making his final appearance in 1976. He was never booked in a career spanning 628 games, a statistic which ranks him fifth in United's all-time appearances chart.
He also played in the team which beat Barcelona home and away in 1966.
A statement on Dundee United's official website read: "As well as being a club legend, Doug Smith was a true gentleman, on and off the park, and highly respected and admired by all those who made his acquaintance.
"Our sympathies and thoughts are with his family and friends at this sad time, particularly David and Louise.
"The club flag is flying at half mast and Dundee United has approached the footballing authorities to request an appropriate mark of respect prior to kick-off on Sunday."
United play Dundee in the SPL at Dens Park on Sunday.
The 21-year-old former Arsenal trainee was a constant threat down the Glovers' right flank and Johnson confirmed that it was not an injury that triggered the defender's withdrawal.
"We brought him off because he looked like he'd run his race, and had done well," he said. "I thought he played well, he got up there and he was a right-back and a right-winger. So we were pleased with him, and I'll let him know that.
"No pros like coming off, to be honest, but they know when I'm disappointed when I take them off, and they know when I'm not disappointed. So he'll be okay."
The 2-0 victory against the 10-man Chairboys was sealed thanks to two first half goals from Ed Upson and then Sam Foley but Johnson was frustrated with his side's second half display.
"It ceased to become a competitive game until probably the last ten minutes, when Wycombe gave it a bit of a go," he said. "Our lads switched off a little bit, which was a bit disappointing.
"Not all of them, but anyway I'll deal with that, as and when I need to. In time, when I write my book, you'll get to know what I really felt about the last 20 minutes!
"Some of the lads that are in that dressing room deserve to be there, (in the next round) but one or two don't."
Smith, who joined the Magpies on a two-year deal in the summer, has been sidelined since being carried off on a stretcher 40 minutes into his debut in the Capital One Cup defeat to Bradford in the first game of the season.
The 24-year-old centre-back has resumed full training and played in a behind-closed-doors friendly at Derby's Moor Farm training ground on Tuesday afternoon, which the Magpies lost 2-0.
Smith came through the game unscathed and manager Keith Curle hopes to have him back in first-team contention in time for the busy Christmas programme.
