Frustration was once again the overriding emotion as Scotland built on the promising displays in defeat to England and Wales with another strong performance against World Cup finalists France, only to lose 23-17 at Murrayfield on Sunday.
Rennie said: "Everyone's just a bit bored of this feeling. It's very frustrating. We are improving week to week and the games are showing that.
"We've got two games left and everyone's going to be targeting two weeks' time to try to put that record right."
It is the first time since 2004 that Scotland have lost five successive Tests, while Andy Robinson's Six Nations record as head coach is two wins from 13 matches ahead of the trip to Dublin.
Should Scotland fail to beat Ireland, who play Les Bleus on Sunday, they will travel to Rome on the final day of the championship seeking to avoid the wooden spoon.
There were further grounds for optimism on Sunday as Stuart Hogg and Lee Jones scored their first Test tries, while the pack went toe-to-toe against their feared opposite numbers, with captain Ross Ford leading from the front.
Rennie was named man of the match, but he wore the battle scars and not a smile after the loss.
The 26-year-old Edinburgh openside added: "Some of our attack was really good and some of our defence was really good, it was just little lapses.
"We knew they were really good with turnover ball and they showed it."
Scotland last savoured a victory in Invercargill on September 14 with a win over Georgia in the World Cup, but in the five matches since have also had victory within reach.
Argentina claimed a last-gasp success, as did England, as Scotland tumbled out of the group stages of a World Cup for the first time.
A new-look England then won the Calcutta Cup at Murrayfield before Wales' class told in Cardiff, but Scotland were culpable on that occasion too.
If the emotions were familiar after defeat to France, the story was similar too.
Rennie, who now has 14 caps, added: "We lacked a little bit of composure at times. Unfortunately when Rory (Lamont) got hurt we went a bit flat just before half-time and to be leading with 20 minutes to go and not know how to close the game out...it was a lack of composure after they scored.
"We turned over the ball several times and we didn't apply pressure onto them in the last 20 minutes and get ourselves into a position to dominate them again."
While much of the focus has been on the new faces in the squad, the pack proved once again they are a match for anyone, not least in the back row where Rennie, David Denton and John Barclay were far from overawed by facing Thierry Dusautoir, Imanol Harinordoquy and Louis Picamoles.
Another severe challenge awaits, with Ireland's Stephen Ferris, Sean O'Brien and Jamie Heaslip equally formidable opposition.
"They were a pretty awesome back row and it's going to be just as hard in two weeks' time," Rennie added.
Rennie has overtaken Barclay in the race for the openside jersey, but the latter proved to be at home on the blindside flank against France and it is a combination that is likely to continue at the Aviva Stadium.
"There are things I can improve on. I really liked playing with Barclay and Denton," Rennie added.
"Dents is a big unit who can go forward and John defensively and in attack is a smart player. If I'm in the wrong place he will hopefully be there or vice versa."
Scotland now have a week off to contemplate how to turn around their campaign, while Ireland travel to Paris for the second time after the original fixture was postponed due to a frozen pitch.
"I hope they're a wee bit tired by then, that wouldn't be a bad thing," Rennie said. "But with their squad they'll be a hard team to beat no matter what."
Scotland suffered several injuries against France, with Lamont (suspected broken leg), Mike Blair (dead leg), Greig Laidlaw (concussion) and Jim Hamilton (calf) all requiring treatment.
Lamont's injury will mean a reshuffled backline once more, but Max Evans (ankle) and Joe Ansbro (back) could be in contention for Dublin.