Naismith was substituted on 62 minutes with a tight calf and Smith departed ten minutes from full-time, also due to a calf-related issue.
The club captain is rated doubtful for this Saturday’s vital Championship match with Dundee at Tynecastle Park. However, hopes are that right-back Smith will be available.
Both players sat out training today and will continue to rest until Thursday at the earliest.
“We expect Michael to train on Thursday. We are just letting his problem settle down for a couple of days,” manager Robbie Neilson told the Evening News.
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“He had a tight calf and was feeling his Achilles a bit over the last week and it flared up during the game on Friday.
“He could have played on but the area was getting stiffer. Hopefully we’ve brought him off in time to make sure he’s okay for this weekend.
“Naisy could potentially train on Thursday as well, although he is more touch-and-go for the weekend. We’ll need to see how he is nearer Saturday but I’m fairly sure we will have Michael.
“Liam Boyce also had a wee niggle after the Inverness game but he will train tomorrow and should be fine.”
Three successive 1-1 draws increase Hearts’ desire for a win, which would take them a step closer to automatic promotion back to the Premiership.
Dundee will also want points in Edinburgh having failed to win any of their last four matches. They host Inverness Caledonian Thistle at Dens Park on Tuesday night – one of three games in hand they have over the league leaders.
“We want to get back to winning ways and back to scoring goals but we know we lost against Dundee last time,” said Neilson. “We had a great result at home against them in the first league game but away from home it was a different story.
“We are looking for a win after three draws but they are exactly the same. They are four games without a win at the moment.”