The Iron are currently sixth in the National League, one point and one place outside the play-off spots.
"I thought we asked a lot of questions of a very good Barrow team," Cowley told BBC Essex.
"When you come off the back of a six or seven-hour journey and you concede a goal after five minutes it's always going to be tough."
Barrow extended their unbeaten league run to nine games with the victory, and although Braintree's losing run extended to three games, Cowley remained positive.
"What we've done so far has been nothing short of remarkable," he continued. "But if anyone thought this journey was going to be easy, then they're living in cloud cuckoo land.
"We're a part-time team. This is our toughest challenge to date, but we're going to embrace it. We're going to enjoy it and see where it takes us."

The 26-year-old will join Wednesday on a permanent transfer in the summer for a fee believed to be £10m.
The Owls had to wait until Wednesday for the English Football League to decide if the deal had been completed by Tuesday's 23:00 GMT deadline.
Rhodes scored six goals in 24 league appearances for Boro after joining from Blackburn for £9m in January 2016.
However, the Scotland international, featured just six times this season and failed to score.
He started his career with Ipswich and had loan spells with Oxford, Rochdale and Brentford before joining Huddersfield in July 2009.
Rhodes scored 73 goals in 124 league appearances for the Terriers and helped them to promotion from League One in 2012.
Blackburn paid the Terriers £8m for him in August 2012 following their relegation from the Premier League.
He moved on to Boro last January after scoring 83 goals in 159 league games for Rovers and helped Aitor Karanka's side win promotion to the Premier League.
Rhodes' father, Andy, is the goalkeeping coach at Hillsborough.
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Knox, 30, has arranged a practice round at Augusta with the 1988 winner.
"It's not every tournament you have a fellow Scot and past champion to show you around," Knox told BBC Scotland.
"I'm looking forward to it and hopefully he'll give me some great insider tips that he's learned over the years that might help me."
Lyle, 58, qualifies as a winner of the Green Jacket, and US-based Knox is the only other Scotsman in the field.
Inverness-born Knox leapt up the rankings in November with victory at WGC-HSBC Champions event in Shanghai and is currently No.34 in the world.
"I still can't quite believe I'm playing at the Masters," he enthused.
"Growing up watching it on TV, now it's my turn to play. It's truly an amazing honour."
Knox has had a taste of the other majors, finishing in a tie for 45th at the US Open in 2013, featuring at the US PGA Championship in 2014 and 2015 and making his Open debut as a reserve at St Andrews last year.
"I've only been to Augusta once before," explained Knox, one of British golf's most promising players.
"It's the most famous course in the world pretty much. Obviously, St Andrews is right up there too.
"Being the first major of the year and with all the history, Augusta just has this hype around it and golf is in a great place right now with so many young, amazing players.
"There's such a buzz around the tournament. The crowds seem amazing and then there's the condition of the course.
"The whole thing is magical, a golfer's dream, and I can't wait to be a part of it."
Braintree manager Danny Cowley said the task ahead of his team is "a brilliant challenge" after the defeat at Barrow.
[NEXT_CONCEPT]
Sheffield Wednesday have signed Middlesbrough striker Jordan Rhodes on loan until the end of the season.
[NEXT_CONCEPT]
Russell Knox aims to tap into the experience of former champion Sandy Lyle as he prepares to make his Masters debut next week.