South Africa international Hougaard kicked a hat-trick of penalties as Tigers claimed a bonus point from a 15-9 defeat to finish top of Pool 3.
The result booked the two-time Heineken Cup winners a home quarter-final against Bath Rugby, which will be played on the weekend of April 10-12.
Hougaard said: “We are going through and we topped the pool – a very tough pool.
“The circumstances, coming away from Ospreys and getting a point to qualify, the guys showed a lot of character to do that.
“We are happy to go through from a tough pool and I am really looking forward to the quarter-finals.
“That period before half-time when we were down to 14 men showed the guys' commitment.
“You can call them by their name but the whole team showed their character with one guy off and we knew we couldn't concede a try just before half-time.
“The guys gutted it out and we got through that period without conceding a point.”
Tigers are next in action in the Guinness Premiership at London Wasps on Sunday, February 15 (5pm) and return to Welford Road on Saturday, February 21 when Worcester Warriors are the visitors (kick-off 3pm).
Tickets for all remaining home fixtures are available now from the Tigers ticket office. Contact the hotline on 08701 28 34 30, book online or call in at Welford Road.