The Blues made an impressive start to their Heineken Cup campaign with a 26-20 victory over Racing Metro in Paris, the scoreline not reflecting their superiority, with the likes of World Cup returnees Sam Warburton, Bradley Davies and Gethin Jenkins making an impact.
But the Exiles suffered a surprise 20-19 home defeat at the hands of Edinburgh, and another loss on Friday night would leave Toby Booth's side with a mountain to climb if they are to secure a quarter-final berth.
And Burnell, who has brought Dafydd Hewitt and Paul Tito into his side in place of injured Jamie Roberts (knee) and James Down (fractured and dislocated ankle), knows the Blues will need to kick on again to subdue the Irish backlash.
"You have to win your games in this competition, because they are all good sides," he said.
"There will be reaction from them, they know they have to come here and win.
"If they don't they then have to face Racing Metro back to back next month, and you don't want to be trailing by two games in a competition like this.
"We were elated with the win in Paris but on Monday morning it was back to the grindstone to focus on London Irish, we know we will have to go up another gear this week because they will be hurting after their defeat."
Burnell expects Irish to provide a different threat from the physical and direct approach of Racing, and has highlighted line-out technician Nick Kennedy and creative fulcrum Dan Bowden as critical figures.
"Their set-piece is very good," he said.
"Their scrum went well last week and Kennedy runs the line-out well for them. Bowden the fly half is an innovative player and has a lot of skill, while Tom Homer is a fantastic kicker so they will pose a threat."
Elsewhere in Pool Two, Edinburgh host Racing Metro at Murrayfield as they look to build on that excellent victory at the Madejski Stadium.
Pool One also sees an intriguing Anglo-Welsh clash as the Scarlets travel to Franklin's Gardens to face last season's beaten finalists Northampton.
The Scarlets, unbeaten in six games after last weekend's home win over Castres, can boast a backline filled with the talents of George North, Scott Williams, Rhys Priestland and Jonathan Davies, but whether they are given the chance to showcase their attacking flair will depend on their forwards subduing a gargantuan Northampton pack.
The Saints, so cruelly denied an opening win in Munster by Ronan O'Gara's drop goal at the end of an extraordinary 40-phase passage of play, have one of the most fearsome packs in the game which includes Dylan Hartley, Soane Tonga'uhia, Courtney Lawes and Tom Wood.
The Scarlets' lack of forward grunt ultimately proved costly during last term's European effort, and captain Matthew Rees has highlighted hooking rival Hartley as a man the visitors will need to subdue.
He said: "Dylan Hartley is massive for them - if he plays well the whole team plays well. He will be disappointed not to have been England's first choice during the World Cup and will want to make a statement but I'm looking forward to the challenge.
"You play against these players a lot for your country and it's good to face them in the Heineken Cup.
"Their whole pack from one to eight is really important - Soane Tonga'uhia, Brian Mujati, Courtney Lawes, Tom Wood and Roger Wilson are massive for them."
Saints boss Jim Mallinder, one of the early favourites to succeed Martin Johnson as England manager, has named an unchanged side and wants Northampton to get over their Thomond Park disappointment by chalking up a first win in the pool.
"Games like last Saturday's don't disappear from your mind straight away, but you learn very quickly in this game to move on," he told the Saints website.
"Myself and the other coaches have been very pleased with the reaction of our players in training this week. We know that we have been playing well and everyone has been positive in their attitude towards Friday's game."
Friday's other Heineken Cup fixture sees Clermont Auvergne look to get back on track following defeat to Ulster when they host Italian side Aironi in Pool Four.
Meanwhile, in the Amlin Challenge Cup, Sale play host to Spanish champions La Vila, while Stade Francais clash with Bucuresti.
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