Heung-Min Son's 62nd-minute winner was enough for Leverkusen to claim a crucial Bundesliga win, moving seven points clear of second-placed Borussia Dortmund, who face Werder Bremen on Saturday.
Hyypiä praised his team for continuing to fight as Leverkusen maintained their record of being unbeaten in the league at Mönchengladbach since February 1989.
"In the end Gladbach exerted a lot of pressure but my team fought very well. I don't know how many shots we blocked but I think a lot," the Finn said.
"That was very good that the team showed character today and I'll always take a 1-0."
Son's goal was a screamer on 62 minutes as he took a pass from Sidney Sam before firing into the corner from 25 yards.
Hyypiä was pleased with how his team improved after the interval and the former defender unsurprisingly had no complaints about only one goal being scored.
"I've had a few interviews already and I get the feeling that everybody is disappointed that only one goal was scored today," he said.
"Because everyone expected an array of goals out of a game like this but I think the first half wasn't spectacular. Gladbach had the better chances to score a goal.
"In the second half my team played better. We played better in possession and then Son scored a beautiful goal."
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