The Shrimpers kicked off their National League campaign with a 3-0 win against Armstrong's team.
But, despite being disappointed by his own side's performance, Armstrong was quick to give Blues praise.
"We can't be looking for excuses when we just didn't turn up," Armstrong told the club's YouTube channel.
"It's not going to be fixed overnight and we have to be patient but they're one hell of a good side.
"You can see they're going to be up there without any shadow of doubt.
"Kevin (Maher) has strengthened his team after just missing out on promotion last year so we knew it would be tough but it's the manner of it I don't like and can't accept."
The Shrimpers dominated the majority of the match against a new-look Gateshead who have endured a summer of change on and off the pitch.
And Armstrong was clearly frustrated at the final whistle.
"It's disappointing the lads didn't perform anywhere near the levels we know they're capable of," said the former Middlesbrough forward.
"I think it was down to fear.
"There was no conviction in any of the play and the three goals we gave away were easily avoidable.
"We gave them the goals really and that was the biggest problem."
The Shrimpers took full advantage of Gateshead's poor defending to secure all three points.
And Armstrong admitted Blues deserved the win.
"They were better than us and you can't take anything from them," said Armstrong.
"They worked harder than us, they ran harder than us and sadly they wanted it more than us which is the most disappointing thing.
"It's a wake up call for us because I think they thought they could just go out and play their football but I've told them time and time again that teams just don't give you that time."
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