By Gabriel Tan
A second-half brace from Yasuhiro Yamakoshi condemned the Tigers to a losing start to their Group B campaign at the Jurong East Stadium, meaning they will now need to beat Geylang United on Monday to stand any chance of progressing to the knockout round.
However, Stewart insists he remains confident his side have what it takes to see off the Eagles at the Toa Payoh Stadium based on what they have achieved so far this season.
"Of course we have to be confident," the Australian told ESPNSTAR.com. "And we will be.
"We have a game at home on Monday and we've had a good season so far, so why shouldn't we be confident?
"We will definitely be up for the match."
Despite the defeat, the former Gombak United boss reveals he was pleased with the effort his players displayed and admits they ultimately lost to two extremely good strikes from Yamakoshi.
"We battled really hard and defended really well but in the end we lost to two good goals," Stewart conceded. "Both were quality goals - it's not that we didn't play well.
"We could possibly have taken our chances in the first half but that would be being really harsh on the boys. The energy and work rate was just superb."
And while Stewart admits the Great Eastern-YEO's S.League remains Balestier's priority, he has keen to stress he is taking the League Cup seriously as well.
"We're not trying to disrespect the League Cup and as you saw tonight [Friday], I put out my strongest XI," he added. "We're still going into every League Cup game looking to win it."
"But the league remains our main priority - it shows you where you are over a prolonged period of games."
Albirex coach Koichi Sugiyama was especially pleased with his team's performance, which was the latest in a run of excellent results that have seen them go top of the S.League.
"In this month, we have had six games and in every one of them, the players have been playing very well," the Japanese said. "I have to praise them for that.
"The level of performance hasn't dropped at all and that is important for us."
And despite looking set to challenge for silverware on two fronts, the former Urawa Red Diamonds defender isn't keen on looking too far ahead.
"We will only look as far ahead as the next game," Sugiyama added. "We want to take things one step at a time."
Following Balestier's game against Geylang next Monday, Group B action will conclude three days later when the Eagles entertain Albirex.