Smithies proved instrumental as Cardiff kept a tenth clean sheet of the season en route to a 2-0 victory but the Huddersfield-born goalkeeper admits it might have been different but for Bamford's inadvertent block at the end of the first-half.
Following a cross into the area from Tyler Roberts with United 1-0 down, Jack Harrison's fierce low strike towards the bottom left corner had Smithies scrambling across his line, with the 30-year-old fearing he would not keep the shot out until it hit Bamford.
Smithies then eventually gathered - with Bamford offside in any case - and Leeds were unable to make any sort of breakthrough despite 17 attempts at goal of which only three were on target.
Reflecting on the incident with Bamford, Smithies said: "The way I saw it, I think that the initial shot might have been going in.
"I was sprinting across my line and I sort of gambled just to fill as much of the goal as I could.
"I think Bamford sort of touched it into me almost and I think he flicked it on to my leg.
"I said to him 'that was going in' and he said 'I was trying to get out of the way of it' so maybe he didn't mean it but he was offside in the end anyway."
Smithies also made a particularly smart save in the second half when racing across his line to keep out a powerful shot at a tight angle from Tyler Roberts.
"I had just seen how hard the lads had been running and how much they had put in," said the keeper.
"They were putting their bodies on the line as well and that was my opportunity to pay them back and put my body on the line and show willingness and thankfully it managed to smash me in the chest and stay out."
Asked how he saw the automatic promotion race as part of a weekend that saw Leeds slip to second on goal difference behind West Brom but stay seven points ahead of third-placed Fulham, Smithies reasoned: "I think in this period of nine games it's almost too early to call after one game how teams are going to react.
"There may be upsets and some teams may have prepared better than others.
"It's obviously been disruptive in all clubs.
"I do expect Leeds to bounce back from that but my main focus is on what we are doing and we are really pushing for them play-offs now."