The Dark Blues are undefeated in their last three SPL games and despite the 14-point gap which separates them from second-bottom Hearts, John Brown's side are refusing to give up hope of avoiding relegation.
Baird put them ahead with a well-taken 12th-minute goal against Caley Thistle only for the visitors to hit back through Billy McKay's late headed equaliser.
But Baird wants to see the SPL's bottom club carry on their positive results on late with eight games remaining between now and the end of the season.
Baird said: "It's just a case of trying to keep it going. That has got to be the aim and that's what we're all focusing on.
"We're playing with a bit more confidence and that's what happens when you get a few results in your favour.
"It's going to be tough obviously but we'll try and remain positive in every game and see what happens.
"We've given ourselves something to build on so it's up to us to take this into the derby with Dundee United next weekend."
Brown insists there's no pressure on his players for the run-in so hopes that can continue to help them.
He said: "Nobody really expects us to do it as it's a big gap. I keep telling the players to go out and enjoy their football as much as possible.
"I think that is paying off and long may it continue.
"The players have given me everything they have ever since I came in so I'm delighted with their effort.
"We're trying to go for victories as much as possible and won't change in that respect.
"That is what we need more than anything in our situation."
Inverness manager Terry Butcher watched his side claim a point through fans' favourite McKay but had little praise for his men.
Butcher said: "There weren't too many positive to take from that.
"We have to be honest about that as it was one of those days.
"We have a big game coming up against Ross County next weekend so we won't need any added incentive for that one.
"It's a derby so we have to be up for it and do much better than we did against Dundee."
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