Taylor released a statement on the club’s website after they were beaten 3-1 in the FA Cup second qualifying round on Saturday suggesting Cowan had not acknowledged his side’s display.
The Bedford boss was unimpressed by Cowan’s claim that his side could have won by more goals, claiming “it made a mockery” of his side’s performance.
Cowan countered Taylor’s views, which also brought into question the homework carried out by the Bucks boss ahead of the tie.
“I felt I was very respectful towards them and could not have done any more research,” said Cowan.
“Their players were excellent and did a brilliant job. Bedford came to spoil the game and I say that as a compliment, they did it really well. We did not take them lightly and put out a very strong team.
“I had two reports of them from teams they played and people I know.
“We made it difficult for ourselves as four of my players did not play to the expected levels. My comments were all meant in a positive manner.”
The statement also accused a member of Cowan’s backroom staff of listening outside the dressing room to Bedford’s half-time team talk and taking notes, which Cowan strongly denied.
“I felt we were very complimentary to them,” Cowan added. “When they arrived we made sure they were getting looked after.”
Meanwhile, the Bucks face an away trip to either Warrington Town or Consett AFC in the third qualifying round of the FA Cup on October 6.
The Bucks are now just two wins away from the first round proper.
The replay between Warrington and Consett, who are one tier and three tiers below the Bucks in the pyramid respectively, will be played at Warrington tonight.