The big lock scored one of six tries as the Warriors inflicted a record European defeat on the Tigers at Welford Road. Gregor Townsend's side have advanced from Pool 1 as one of the best runners-up after the 43-0 triumph. And man-of-the-match Tim was delighted to make history for Glasgow.
Speaking just after the final whistle, Tim said: "I feel fantastic, it was our goal to get out of the pool at the start of the season and we've managed to achieve that which is a great feeling. Now we go on to the next stage and give that a go.
"We focused on ourselves a lot this week. When we play our rugby we can beat anyone and we saw that today. It was a really good team performance. The forward pack worked extremely hard and the backs were great as a unit and that's what put them to the sword."
Glasgow scored a total of 85 points against Leicester in their two Pool 1 clashes. Scotland fly-half Finn Russell was central to their last-eight qualification, and he hailed his forward pack for laying the foundations for a destructive attacking performance.
He said: "We knew how physical the game was going to be today and credit to the boys up front because they made it easy for us. Credit to the boys the set-piece and lineout drive was outstanding today.
"We looked at ourselves a lot this week and we knew how tough it would be to come down here and get a win. We knew we would have to play with tempo and play quick, attacking rugby and we did that for the full 80 minutes."