Baxter, whose side are currently enjoying their first season in rugbyÃ¢â‚¬â„¢s top flight, said: “We’d done well away from home but repeatedly come up short, so to see the job through is special.
“We have showed that when you want something badly enough and are prepared to work for it you can succeed.”
The result leaves Exeter in ninth, while Saracens lose ground on leaders London Irish but remain in the play-off positions in fourth.
Baxter was also quick to praise fly-half Ryan Davis, who recently signed from Bath and was instrumental in the sideÃ¢â‚¬â„¢s victory, scoring 18 points.
“Ryan joined us from Bath and while Gareth Steenson was first choice fly-half he worked hard and waited patiently,” added Baxter.
Ã¢â‚¬Å“HeÃ¢â‚¬â„¢s a sparkly individual and a fine goalkicker and I think he did a tremendous job avainst very fine opposition.Ã¢â‚¬Â
Saracens director of rugby Brendan Venter echoed BaxterÃ¢â‚¬â„¢s comments but was unable hide his frustration at his sideÃ¢â‚¬â„¢s performance.
Ã¢â‚¬Å“Their defence was excellent but the bottom line is they played as a team and today we played as individuals,” said Venter.
“From my point of view it’s amazing what you can achieve with a collective will. They came here with a team of unknowns, got stuck into us and deserved to win.”
Venter was also quick to defend under-fire fly-half Alex Goode, who has been heavily scrutinised following the high-profile signing of Gavin Henson last week.
Ã¢â‚¬Å“Alex is growing and learning as a rugby player, he’s in the pinnacle position and he is learning that, perhaps even sooner as first choice than I would have planned.
Ã¢â‚¬Å“Gavin will become available when he finishes on ‘Strictly Come Dancing’ and when that happens he will face three to four weeks of tough training
He added: “It’s a long time since he played first class rugby or any rugby and we must bear that in mind.”
Saracens move on to face a tough challenge against Bath at the Recreation Ground in three weeks’ time while Exeter play host to struggling Leeds.
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