The Bucks were eliminated at the hands of lower-ranked opposition for a third season running after a goalless draw in Suffolk in which they dominated, only for the step three hosts to win 9-8 in the shootout.
The boss admitted his side were guilty of passing up a number of chances to put the third qualifying tie – worth £5,625 to the victors – to bed, as he was left with the feeling it would be Leiston’s night.
“I don’t want to make excuses because ultimately we’ve not been victorious, but it’s another scalp for the FA Cup, I feel,” Cowan said. “I think we had eight chances in the first half that are ‘must score’ and hit the bar numerous times and numerous chances in the second half.
“It’s hard to wrap your head around and does smack of the FA Cup.
“It should never have got to penalties, we should have been out of sight. Credit to my players for the character and professionalism for keep doing what they were doing.
“The only thing is we’ll rue missed chances.”
Telford’s Adam Walker and James Hardy struck the woodwork late on as the breakthrough proved elusive.
The boss continued: “Credit to Leiston, they had a gameplan and would appreciate we’re the better side on any given day and made it difficult.
“We were quite aware the pitch would tear up and it did. It was very difficult conditions, but for both teams. We wanted to play between the lines and credit to the lads for keep doing it.
“It was really fruitful as we were getting many chances but I can’t put my finger on why we haven’t taken the chances. Again it just smacks of the FA Cup. It’s their year I suppose.”
Cowan, who named an unchanged XI for the third match running, said: “Even scoring eight penalties we couldn’t get it over the line.
“It’s hard to criticise my players because they’ve shown immense professionalism, got on with the journey, done everything I’ve asked of them, the only thing I’d ask is game management which is being really picky.
“But more so just really take chances. You stick one away and it’s an easy night but credit to Leiston.
“We shouldn’t have allowed it to get to penalties, because it’s a lottery, the toss of a coin. We’ve only got ourselves to blame. We’ve got to finish chances.
“It’s tough, I don’t want to criticise my players, they’ve worked extremely hard and carried out the gameplan but ultimately it’s about putting it in the back of the net.”
Cowan’s side have made a strong start to the National League North campaign, taking four points from six after facing Brackley and Blyth Spartans and turn their focus to Saturday’s visit of Gateshead.