Agnew said Karanka's departure was a "difficult and very emotional day" but did not think the former manager was exhausted after doing an "incredible" job, including securing promotion to the Premier League last season.
Stewart Downing was at the heart of Aitor Karanka's sacking at Middlesbrough.
With Boro now 19th, without a league win since mid-December and having scored only three goals in their last 10 league games, Agnew faces quite a challenge and knows it. "Keeping us up would be the single biggest achievement of my life", he acknowledged.
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The former Tottenham boss has not worked in the Premier League since leaving Queens Park Rangers in 2015 but is said to feel confident his experience would help keep Boro up. "I see myself as being a creative coach, slowly but surely I know I'm capable of drip-feeding ideas into the group that will pay dividends", he said.
Asked if it was similar scenario to Claudio Ranieri's dismissal at Leicester Mourinho replied: "In this case, I know the names!"
In the first year he arrived, the team was going into League One and he saved the team.
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With her step father as her trainer and her mother part-owner of the horse she is riding, it is very much a family enterprise. She added: "I've never had a runner in the race before so to train the victor - I don't know when I'll come down to earth".
'In the second year, he took the team to Wembley to play the play-off final.
Agnew will oversee this weekend's clash with Manchester United and the Boro hierarchy will have two weeks before their next game due to the global break, giving them time to find a replacement.
Assistant head coach Steve Agnew took over first-team duties ahead of the trip to Old Trafford.
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The former Republic of Ireland worldwide continued: "There are names [being mentioned] galore, but I would personally go for Martin O'Neill, that would be my gut instinct".