The narrow win in Ireland was all the more impressive following a run of three successive defeats in the Heineken Cup and the LV= Cup having started the year positively with victory over Zebre in the league and an epic 15-15 draw with Leicester Tigers in Europe's elite competition.
But while Rees was the first to praise his players for the win in Ulster he is fully aware of the importance of another victory on Friday as the RaboDirect PRO 12 enters the business end of the season.
"We came back in the other day and the first thing we referenced was well done," said Rees, whose side have been impressive in the league, winning their last five RaboDirect games since losing 13-23 to Edinburgh at Murrayfield on November 23.
"But we move onto a tough away game and Connacht presents a different but probably in some ways more difficult challenge and we need to go there and pick up points because there is a tough run of fixtures and this will be the start of it."
Ospreys will be boosted by the return of forwards Alun Wyn Jones and James King, who are among eight players who have returned to their regions after being released from Wales' Six Nations squad.
Jones came off the bench in Ospreys' win over Ulster - his first appearance since injuring a shoulder in November - and Rees is delighted to have the duo back.
"He came off the bench last week and was a great impact for us," he added.
"We are delighted to have him in the group because whether we're playing a top end European game or RaboDirect, Alun Wyn is Alun Wyn.
"He's 100 per cent in everything he does, he's been throwing himself around tackles and he's the type of leader that epitomises what we're about."
Connacht meanwhile, go into the game having won two lf their last four matches while their last five games have been won by the home side on the day.
Eric Elwood has made three changes to the side that lost to the Scarlets last time out with Robbie Henshaw, fresh from helping Ireland Under-20s to victory over England, returning at full-back.
Tiernan O'Halloran returns to the right wing while Danie Poolman replaces Fetu'u Vainikolo on the left wing.
The front five in the pack remains unchanged with Nathan While captaining the side and recent returnees John Muldoon and Willie Faloon, who were brought off the bench against Scarlets come back into the back row.
Gavin Duffy is named on the bench and could make his 150th Connacht appearance at the Sportsground.
At Sportsground, 7.45pm. Live on TG4
Referee: Guiseppe Vivarini (FIR, 5th competition game)
Assistant Referees: Michael Black, Will O'Connor (both IRFU)
Citing Commissioner: Tom McCormack (IRFU)
TMO: Jude Quinn (IRFU)