Monk lost his job on Saturday night after Boro beat Sheffield Wednesday 2-1 at Hillsborough and was replaced by Tony Pulis on Boxing Day.
Boro had lost four of their previous six games prior to the Wednesday win but were only three points off the play-offs when he got the call from chairman Steve Gibson.
Monk said in a statement released through the League Managers Association: “I was saddened to be informed by Middlesbrough Football Club on Saturday evening that my services as the club’s manager and those of my staff were no longer required.
“Just hours earlier we had enjoyed what we felt was the side’s best away performance of the season in our win against Sheffield Wednesday.
“My staff and I were surprised by the timing of the decision. Of course, we expected to be higher up the league and to be seeing more consistent performances by this stage.
“I do accept my responsibility for that. But the feeling amongst everyone in the dressing room after Saturday’s game was that it was the turning point in our season, knowing that there was still half of the campaign remaining.
“Particularly in view of the fact that we were only three points off the play-off places with some really winnable games coming up, we felt that we would be able to make up more ground on the teams occupying the top spots.
“We were all really confident that we could still achieve the target of promotion to the Premier League, which was set at the start of the season.
“We knew that the great commitment levels being shown by the players on a daily basis towards our work would pay dividends. I really hope that the club can now keep moving up the league.”
Pulis was announced as Monk’s replacement early on Boxing Day and he was present to watch a 2-0 win over Bolton, a result which moved them up to seventh, still three points off the play-offs.
The 38-year-old has been linked with a return to Swansea and also the Sheffield Wednesday job after Carlos Carvalhal also left his position after Saturday’s game.