The English side gained the consolation prize of a place in this season's Amlin Challenge Cup last eight after ending their Heineken Cup Pool 2 campaign with a 32-23 win at Rodney Parade.
They now drop down into the second-tier tournament where they will be joined by five group winners of that competition and two other Heineken Cup sides.
"There was a quarter-final place at stake today, and it is a big thing," said Redpath.
"It was a big match for us. A European quarter-final gives us something to look forward to. We haven't had a great record away from home. We got the four tries that we needed."
Fijian flanker Akapusi Qera was Gloucester's key man, scoring a hat-trick of tries before the bonus point was sealed through a 74th-minute penalty try.
Redpath added: "I was frustrated with our first-half performance – we did not look energised – but we were a lot stronger in the second period, particularly the forwards. To score four tries away from home is a good return. Qera is a handful when he plays like that."
The Dragons, six points clear at the break, managed a Rhodri Gomer-Davies try and a late Ashley Smith touchdown in addition to two penalties, a drop-goal and a conversion from James Arlidge, and a Jason Tovey conversion.