Jones, who finished off a fine move for Glasgow's third try in the comeback win over the Bulls, believes people will now start to take the Scotstoun side more seriously.
"For Glasgow, it puts us on the map," Jones told the BBC Rugby Union Weekly podcast. "We've been competing with the top end of the URC for a while but it seemed as though we weren't taken that seriously.
"All the focus was on the Irish and South African sides. To be able to string together this final run shows what we can do. That's huge for us and gives us huge belief going forward."
Jones, who is in Scotland's squad for the summer tour of the Americas, believes Glasgow's win could also spur on the national side.
"For Scottish rugby, we've won big games in the past but never managed to string the games together," he added.
"We say that every Six Nations, that we want to string performances together in order to go on and win something.
"That's what we've done here. That gives us huge belief with Glasgow and with Scotland. This could be something that propels both teams on in the future."
Jones says the try from Scott Cummings just before the break in the final as the pivotal moment as Glasgow cut the Bulls' lead to 13-7.
"The biggest thing was that try we scored before half-time, that was huge," he said. "Had we gone in 13-0 down, it would have seemed a bit tougher. That gave us a huge boost.
"Looking around the changing room there was a general belief that we were going to win. It felt like it was never in doubt.
"Last year, that would have rattled us and we would've lost faith. This year we've been more mature, sticking to plan, and executing well. Almost everything worked."