Laidlaw struck a last-minute penalty to finally fend off the French team and tie up a victory that sent a Scottish side into the last four for the first time.
But he also credited the 37,881 spectators, a record for a Heineken Cup quarter-final in Britain, for helping them through a thrilling finale.
“The fans were immense,” Laidlaw said.
“The noise they created in the stadium was amazing, from start to finish, but towards the end of the game they were just incredible.
“It was an exhausting and extremely physical game and in the last 10-20 minutes they made a huge difference as we battled on for the win.”
Edinburgh made a perfect start to the game when Mike Blair pounced on Laidlaw’s up-and-under to cross over inside two minutes, with the fly-half converting.
Lionel Beauxis reduced the deficit with two penalties and Edinburgh temporarily went down to 13 men when Allan Jacobsen and then Ross Rennie received yellow cards.
Beauxis soon kicked a penalty and Timoci Matanavou scored a solo try to put the French side in the lead, but they could not add to their tally and Laidlaw’s drop goal reduced the arrears to four before half-time.
Despite losing Blair to a shoulder injury, Laidlaw kicked Edinburgh into the lead within 10 minutes of the restart and the hosts restricted Toulouse’s chances before the stand-off sparked jubilant scenes with his final kick.
Former Munster player and current Edinburgh head coach Michael Bradley admitted his side had ridden their luck but always believed they could cause an upset.
“We have the ability to trouble anybody on our day and there was plenty of confidence in the side,” Bradley said.
“We’ve played a lot of good rugby in this competition, and under pressure we’ve been able to deliver in critical moments in matches in the pool stages.
“And I think we rode our luck a little bit in it as well. Going down to 13 men was not wise.
“You could lose a game quite comfortably if you are down to 13 men for 10 minutes. We could easily have lost the game then.
“We were obviously very fearful of Toulouse’s ability, in particular up front, but we also felt that just to play Toulouse one way would be too easy for them to defend.
“So what we tried to do was use multiple tactics, sometimes going wide, sometimes going close. We kicked more ball than we would normally kick because Toulouse’s defence is very strong and they score a lot of tries from turnovers.
“Their breakdown work is excellent, so we just had to keep varying the target.”
Scorers for Edinburgh: Try: M Blair. Con: G Laidlaw. Pens: G Laidlaw (three). Drop goal: G Laidlaw.
Scorers for Toulouse: Try: T Matanavou. Pens: L Beauxis (three).
EDINBURGH: T Brown; L Jones, N De Luca, M Scott, T Visser; G Laidlaw (capt), M Blair; A Jacobsen, R Ford, G Cross, G Gilchrist, S Cox, D Denton, R Rennie, N Talei.
Replacement: J Thompson for M Scott (9-17), K Traynor for Jones (32-35), C Leck for M Blair (41), K Traynor for A Jacobsen (60-64), S McInally for R Rennie (69), R Grant for N Talei (69).
Yellow cards: A Jacobsen (25), R Rennie (27).
TOULOUSE: Y Jauzion; T Matanavou, F Fritz, Y David , Y Donguy; L Beauxis, L Burgess; J Poux, W Servat, C Johnston, Y Maestri, P Albacete, J Bouilhou, Y Nyanga, T Dusautoir (capt), L Picamoles.
Replacements: G Galan for Picamoles (47), C Tolofua for Bouilhou (48-56), C Poitrenaud for Fritz (51), D Human for J Poux (53), Y Montes for Johnston (60), J Doussain for Burgess (66), G Lamboley for Y Maestri (70), C Tolofua for W Servat (73).
Yellow card: W Servat (45)
Referee: Nigel Owens (Wales).