He said: "We dug in a lot and we had belief. The match lasts 80 minutes and we're not going to give up after 40 minutes if it's not going our way.
"When I came on I was just focusing on getting the ball in my hands. I wanted to get on the pitch, instead of sitting on the bench. It was a big team effort. We knew we needed to get possession of the ball and get it up the field."
Matavesi was brought on to replace Alex Grove with little over 20 minutes remaining and went over for a 67th minute try.
The Northampton defence failed to deal with the impact of substitutes Matavesi, Josh Drauniniu and Jonny Arr and all three went over the whitewash for tries.
Replacement Ollie Hayes added a fourth try after 80 minutes and Andy Goode kicked the conversion to help Warriors record a try bonus point and bonus losing point.
Matavesi added: "I was pleased to get a try and the team were delighted to get the two points, maybe it could have been four or even five points if we had a bit longer. We were looking for the win so it's still disappointing in that respect."
Matavesi was also quick to pay tribute to the substitutions who came on and changed the game.
"Craig Gillies came on and caught all his restarts Josh Drauniniu came on and made some great forward runs and Matt Kvesic broke a few lines so it shows that players on the bench can make a big impact," he added.