The club showed marked improvements against Ospreys at the Liberty Stadium last weekend but came away with just a losing bonus point after a late Justin Tipuric try snatched the win for the hosts in the dying seconds (26-19).
Now, with his former club coming to the home of Edinburgh Rugby, head coach Michael Bradley is adamant that, while improvements are welcome, performance means little without points.
He said: "The boys stuck in to the Ospreys match for the full 80 minutes which was important for us as it was something we targeted going in to the match. We now have to maintain that in all our games this season.
"Our scramble defence and general effort on the day was a huge improvement and we got ourselves into a position to win the game but unfortunately didn't take it.
"We now need to a repeat that commitment and hunger and take any opportunities to win this game.
"It's very important that we get a 'W' on the board tomorrow, no matter how we do it, we need to get a win."
Connacht come to Murrayfield with two wins from two this season against Treviso away (11-9) and Scarlets at home (13-11) and will be keen to continue that run with a win over their former boss on his new patch.
Bradley added: "I know Connacht very well and I've been getting plenty of communication from them on the fact that they're looking down on us in the table.
"Connacht are always difficult when they have confidence and, rightly so at this point in the season, they should be very confident coming here tomorrow night."
Bradley has made four personnel changes to the side that started against Ospreys last weekend with versatile captain Greig Laidlaw moving to the stand-off role he operated so successfully at the end of last season to form a new partnership with Chris Leck, who earns his first competitive start.
Lee Jones lines up on the wing in place of the injured Simon Webster (hamstring) while Jack Gilding (prop) and Steven Turnbull (lock) come into the pack.
The squad also welcome the return of promising young back-row forward, Stuart McInally, from a foot injury.
Edinburgh Rugby team to play Connacht at Murrayfield tomorrow (Friday 16 September, kick-off 7.30pm), round three of the RaboDirect PRO12
15 Tom Brown
14 Lee Jones
13 Jim Thompson
12 James King
11 Tim Visser
10 Greig Laidlaw CAPTAIN
9 Chris Leck
1 Kyle Traynor
2 Steve Lawrie
3 Jack Gilding
4 Grant Gilchrist
5 Steven Turnbull
6 Sean Cox
7 Roddy Grant
8 David Denton
Substitutes
16 Andrew Kelly
17 Robin Hislop
18 Shaun Knight
19 Esteban Lozada
20 Stuart McInally
21 Alex Black
22 Gregor Hunter
23 Matt Scott
Guinness PRO12
Suite 208, Alexandra House,
The Sweepstakes
Ballsbridge, Dublin 4, Ireland